In this paper we describe a share package XMod of functions for computing with finite, permutation crossed modules, cat1-groups and their morphisms, written using the GAP group theory programming language. The category XMod of crossed modules is equivalent to the category Cat1 of cat1-groups and we include functions emulating the functors between these categories. The monoid of derivations of a crossed module X, and the corresponding monoid of sections of a cat1-group C, are constructed using the Whitehead multiplication. The Whitehead group of invert- ible derivations, together with the group of automorphisms of X, are used to construct the actor crossed module of X which is the automorphism object in XMod. We include a table of the 350 isomorphism classes of cat1-structures on groups of order at most 30.