We propose a computational design approach to generate 3D models composed of interlocking planar pieces. We show how intricate 3D forms can be created by sliding the pieces into each other along straight slits, leading to a simple construction that does not require glue, screws, or other means of support. To facilitate the design process, we present an abstraction model that formalizes the main geometric constraints imposed by fabrication and assembly, and incorporates conditions on the rigidity of the resulting structure. We show that the tight coupling of constraints makes manual design highly nontrivial and introduce an optimization method to automate constraint satisfaction based on an analysis of the constraint relation graph. This algorithm ensures that the planar parts can be fabricated and assembled. We demonstrate the versatility of our approach by creating 3D toy models, an architectural design study, and several examples of functional furniture.