This paper presents a method to determine whether an assembly of planar parts will stay assembled as it is pushed over a support surface. For a given pushing motion, an assembly is classified into one of three categories: (P = possible) any force necessary to assure stability of the assembly can be generated by the pushing contacts; (I = impossible) stability of the assembly is impossible; and (U = undecided) pushing forces may or may not be able to stabilize the assembly. This classification is made based on the solution of linear constraint satisfaction problems. If the pushing contacts are frictionless, motions labeled P are guaranteed to preserve the assembly. The results are based on bounds on the possible support friction acting on individual parts in the face of indeterminacy in the distribution of support forces. Experimental results supporting the analysis are given.