During the last several years many scientists have worked in the field of kinematic synthesis of spatial mechanisms; see for example: Levitskii and Shakvazian [1], Hartenberg and Denavit [2], Mohan Rao, Sandor, Kohli, and Soni [7]. In this paper the exact synthesis of the RSSR spatial four-bar mechanism is presented. Both finitely and infinitesimally separated positions of the driver and follower are considered. The analytical development leads to a system of linear equations (6) using the free parameter β. This system of equations has solutions if the system determinant FDET vanishes, eq. (9). Solving this determinant, we obtain all ( α, β) combinations which form a basis for the determination of all geometric parameters of the mechanism. The free parameter β is variable between β u and β o and yields an infinite number of theoretical solutions when seven arbitrarily separated input-output positions are prescribed. Therefore, the designer has the possibility of including other constraints such as minimum transmission angle, special geometric demands, realization of an additional input-output position, or velocity or acceleration at a special position of the mechanism. Altogether; eleven separate problems are formulated and solved by use of a digital computer. Some examples are presented which demonstrate this method.