Computer-aided design of assembly processes (Computer aided assembly planning, CAAP) of complex products is an important and urgent problem of state-of-the-art information technologies. Intensive research on CAAP has been underway since the 1980s. Meanwhile, specialized design systems were created to provide synthesis of assembly plans and product decompositions into assembly units. Such systems as ASPE, RAPID, XAP / 1, FLAPS, Archimedes, PRELEIDES, HAP, etc. can be given, as an example. These experimental developments did not get widespread use in industry, since they are based on the models of products with limited adequacy and require an expert’s active involvement in preparing initial information. The design tools for the state-of-the-art full-featured CAD/CAM systems (Siemens NX, Dassault CATIA and PTC Creo Elements / Pro), which are designed to provide CAAP, mainly take into account the geometric constraints that the design imposes on design solutions. These systems often synthesize technologically incorrect assembly sequences in which known technological heuristics are violated, for example orderliness in accuracy, consistency with the system of dimension chains, etc.An AssemBL software application package has been developed for a structured analysis of products and a synthesis of assembly plans and decompositions. The AssemBL uses a hyper-graph model of a product that correctly describes coherent and sequential assembly operations and processes. In terms of the hyper-graph model, an assembly operation is described as shrinkage of edge, an assembly plan is a sequence of shrinkages that converts a hyper-graph into the point, and a decomposition of product into assembly units is a hyper-graph partition into sub-graphs.The AssemBL solves the problem of minimizing the number of direct checks for geometric solvability when assembling complex products. This task is posed as a plus-sum two-person game of bicoloured brushing of an ordered set. In the paradigm of this model, the brushing operation is to check a certain structured fragment for solvability by collision detection methods. A rational brushing strategy minimizes the number of such checks.The package is integrated into the Siemens NX 10.0 computer-aided design system. This solution allowed us to combine specialized AssemBL tools with a developed toolkit of one of the most powerful and popular integrated CAD/CAM /CAE systems.