This paper deals with the kinematic analysis and enumeration of singularities of the six degree-of-freedom 3-RPS-3-SPR series-parallel manipulator. The characteristic tetrahedron of the S-PM is established, whose degeneracy is bijectively mapped to the serial singularities of the S-PM. Study parametriza-tion is used to determine six independent parameters that characterize the S-PM and the direct kinematics problem is solved by mapping the transformation matrix between the base and the end-effector to a point in P 7. The inverse kinematics problem of the 3-RPS-3-SPR series-parallel manipulator amounts to find the location of three points on three lines. This problem leads to a minimal octic univariate polynomial with four quadratic factors.