Both goalkeepers were tested in the first half, Chris Neal denying Cheltenham’s Luke Summerfield with a low save in the seventh minute.
At the other end Scott Brown did well to reach Mark Wright’s shot and Shrewsbury skipper Ian Sharps glanced Matt Richards’ floated free-kick against the outside of the left post.
Shrewsbury had two late chances to snatch the points, with Marvin Morgan striding through to be thwarted by Brown in the 78th minute, before Wright fired the loose ball wide with the goal gaping.
And when Brown could only parry Wright’s shot with seven minutes left it Morgan failed to convert the second ball from close range.
Cheltenham’s best opportunities to win came fell to James Spencer, who drove over after Marlon Pack had sent a fierce volley clear of the crossbar.