Abstract: The strategy of "maximal reasoning+least variables" to solve 3D geometric constraint loop satisfaction problem is presented.The approach of DOF propagation can recognize the geometric constraint loops in the dynamic process of solving constraints.The method of geometric reduction simplifies the loop to a reducibility tree and clarifies the structure of the loop.The vector-loop model with the least variables contained in the constraint equations is created.The variables have unambiguous geometric meaning,so it is easy to assign the initial value to the variables to cope with multi-solution and under-constrained problems.