Abstract: A kinematically indeterminate assembly will usually undergo mechanism movement involving large displacements under external loads, until reaching a configuration in which it satisfies the criterion for immobility of assemblies. This paper presents an algorithm for the computation of kinematically indeterminate assemblies based on compatibility matrices’ singular value decomposition (SVD) with small deformation assumption. In each step, two compatibility equations are established for the initial and temporary configurations, from which the predictor displacements and compensator displacements are respectively obtained. The real mechanism displacements are derived by superposition of the two sets of displacements and the kinematic path is thus tracked. When the assembly arrives at the immovable configuration, the static computation can then be carried out and the final equilibrium state will be gained. Two examples are illustrated, by which the algorithm is proved to be an efficient and accurate way to determine the final state of an assembly without iteration.