A novel 2- UPS + 2- RPU over- constraint parallel manipulator（ PM） is proposed. The two RPU legs of this PM provide four constraints whereas two of them are over- constraints due to the particular arrangement of the joints in RPU legs. Firstly,the constraint forces are analyzed on the basis of the screw theory and the velocity constraint equation of this PM is established,and based on this,the degree of freedom of this PM is analyzed. Secondly,the geometric constraint equations of this PM are established,and the inverse displacement analysis model is provided by using analytical methods. Then,the elastic deformation of the limb is analyzed with the limb constraint wrenches based on calculating deformation and superposition principle at small strain,and the stiffness matrix of the limb constraint wrenches is defined. Finally,the relationship between outer loads and both the line displacement and the angle displacement of the moving platform is set up,and then the matrices of flexibility and stiffness are obtained. It is found that the constrained force / torques have a major influence on the stiffness and elastic deformation of limited- DOF over- constraint PMs,and the elastic deformation are mainly in the axial direction of the constrained force / torques.