Assembly variation should be predicted accurately in the design process of a product to ensure the performance of the assembled parts. One important issue in predicting assembly variation is to search propagation paths along which variation accumulates. In this paper, a new searching algorithm of multibranch propagation paths of assembly variation for rigid body assemblies is proposed. First, the concepts of feature set and relation set are proposed to express the information of geometric tolerances and assembly constraints among features. Second, the actual constraint directions of a reference relation considering the precedence level are obtained. Third, the search of multibranch propagation paths is conducted by intersecting the actual constraint directions of different reference relations. Finally, the accuracy and efficiency of the proposed method are validated by comparing with the commercial computer-aided tolerancing (CAT) software package, 3DCS, for predicting assembly variation of the body structure of an aircraft. The outcomes of the paper can treat geometric tolerances, which overcome the drawback of traditional dimension-chain-based methods in predicting assembly variation. It is expected that a synthetic use of the proposed method and the dimension-chain-based methods can provide a computationally efficient substitute for the classical Monte Carlo simulation in predicting assembly variation.