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This paper presents the stiffness analysis and design of a 3-DOF parallel robot with one constraining leg, which takes into account of elastic deformations of joints and links. The parallel manipulator in this study is made up of three SPS (Spherical-Prismatic -Spherical) legs and one UP (Universal-Prismatic) leg at the center. The role of the UP leg constrains the motion of the moving platform to 3-DOF and the three SPS legs drives the moving platform by three linear actuators. The stiffness matrix is derived as follows. The reaction forces due to actuations and constraints in each serial chain are determined by making use of the theory of reciprocal screws. The stiffness of this manipulator is modeled such that the moving platform is supported by 6 springs related to the reciprocal screws of actuations and constraints. A general 6times6 stiffness matrix is derived, which is the sum of the stiffness matrices of actuations and constraints. Then the compliance of each spring is precisely determined by modeling the compliance of joints and links in a serial chain. Using the suggested methodology, the stiffness of the 3-DOF parallel robot with one constraining leg has been analyzed. Finally, a numerical example of the optimal design to maximize stiffness in a specified box-shape workspace is presented.