A method for treating a complex structure as an assemblage of distinct regions, or sub-structures, is presented. Using basic mass and stiffness matrices for the substructures, together with conditions of geometrical compatibility along substructure boundaries, the method employs two forms of generalized coordinates. Boundary generalized coordinates give displacements and rotations of points along substructure boundaries and are related to the displacement modes of the substructures known as "constraint modes." All constraint modes are generated by matrix operations from substructure input data. Substructure normal-mode generalized coordinates are related to free vibration modes of the substructures relative to completely restrained boundaries. The definition of substructure modes and the requirement of compatibility along substructure boundaries lead to coordinate transformation matrices that are employed in obtaining system mass and stiffness matrices from the mass and stiffness matrices of the substructure. Provision is made, through a Rayleigh-Ritz procedure, for reducing the total number of degrees of freedom of a structure while retaining accurate description of its dynamic behavior. Substructure boundaries may have any degree of redundancy. An example is presented giving a free vibration analysis of a structure having a highly indeterminate substructure boundary.