Shape by Robert Sheckley

Shape by Robert Sheckley (first published as Keep Your Shape, Galaxy, November 19531) sees a spaceship of shape-shifting Glom arrive in Earth orbit; they are on a mission to place a displacer in one of Earth’s atomic reactors to open up a wormhole for an invasion. Previous expeditions have failed.
Before they descend to the surface, the commander of the ship, Pid, addresses his crewmates Ger and Ilg:

“A lot of hopes are resting on this expedition,” he began slowly. “We’re a long way from home now.”
Ger the detector nodded. Ilg the radioman flowed out of his prescribed shape and molded himself comfortably to a wall.
“However,” Pid said sternly, “distance is no excuse for promiscuous shapelessness.”
Ilg flowed hastily back into proper radioman’s shape.
“Exotic shapes will undoubtedly be called for,” Pid went on. “And for that we have a special dispensation. But remember—any shape not assumed strictly in the line of duty is a device of The Shapeless One!”
Ger’s body surfaces abruptly stopped flowing.

This sets up the story’s conflict, which is that, although the aliens on Glom can assume any shape they want, there are strict caste rules which determine those they are allowed to adopt in society—and Pid has learned before his departure that his two crewmates may not be reliable in this respect:

“Ger, your detector, is suspected of harboring alterationist tendencies. He was once fined for assuming a quasi-hunter shape. Ilg has never had any definite charge brought against him. But I hear that he remains immobile for suspiciously long periods of time. Possibly, he fancies himself a thinker.”
“But sir,” Pid protested, “if they are even slightly tainted with alterationism or shapelessness, why send them on this expedition?”
The chief hesitated before answering. “There are plenty of Glom I could trust,” he said slowly. “But those two have certain qualities of resourcefulness and imagination that will be needed on this expedition.” He sighed. “I really don’t understand why those qualities are usually linked with shapelessness.”

After the three of them land on Earth they dissolve the ship (spoiler), and it isn’t long (there are some episodes that play out beside the reactor) before Ilg and Ger disappear. Pid later discovers that Ilg has become a tree and a thinker, and Ger a dog and hunter. Worse, Pid learns that another dog Ger was chasing earlier is a member of a previous Glom expedition.
The final section sees Pid eventually manage to get inside the reactor building, where the alarm is raised and he is pursued by guards. Then, plagued by thoughts about freedom of shape, and just as he is almost able to activate the displacer, he looks out a nearby window:

It was really true! He hadn’t fully understood what Ger had meant when he said that there were species on this planet to satisfy every need. Every need! Even his!
Here he could satisfy a longing of the pilot caste that went even deeper than piloting.
He looked again, then smashed the displacer to the floor. The door burst open, and in the same instant he flung himself through the window.
The men raced to the window and stared out. But they were unable to understand what they saw.
There was only a great white bird out there, flapping awkwardly but with increasing strength, trying to overtake a flight of birds in the distance.

This is a great finish to a good story, and puts this on my list of Sheckley’s best stories (Specialist, Pilgrimage to Earth, etc.).
One of the things that particularly struck me about this piece was how concisely and clearly written it is and, although there is a message here about social conformity, we aren’t continually bludgeoned with it (I shudder to think what a modern day, MFA’d version of this story would look like).
**** (Very Good). 4,550 words. Story links (see footnote 1).

1. The version of the story I read was in The Arbor House Book of Modern Science Fiction, but the original version in Galaxy magazine (as Keep Your Shape) is longer (5,900 words) and has a completely different ending (and one that makes it a much weaker and more pedestrian story).
In the latter version (the story changes from “He studied himself for a moment, bared his teeth at Ger, and loped toward the gate.” on p. 16 of Galaxy, section break bottom right/p. 67 of the Arbor House anthology) Pid first turns into a dog, and then a man, but can’t stand either shape, so eventually changes into a sparrow. As Pid flies towards the reactor building he is attacked by a hawk and, after slipping through its grasp, changes into a bigger hawk and scares it away. Then Pid drops the displacer and flies after the attacking hawk to find how it hovered in the air.
Theodore Sturgeon used to say something along the lines of, “Horace Gold could turn an average story into a good story, and an excellent story into a good story”. One wonders if this is an example.
Story link (Shape, Arbor House, recommended version).
Story link (Keep Your Shape, Galaxy).