A six degree of freedom 4-PRP+3-UPS&PU redundant hybrid machine tool is proposed,and the statics and static stiffness of the machine tool is studied. Firstly,based on the force Jacobi matrix,the static equilibrium equation is presented,and the mapping matrix between the external load and the driving force and the binding force of the branch is solved. Secondly,the binding screw provided by each drive branch and constraint branch is analyzed,the elastic deformation of each rod under the action of the constraint screw is calculated. Finally,the stiffness model of the mechanism is established,and the elastic deformation of each branch is superposed,and then the overall flexibility and stiffness matrix of the mechanism are obtained. Combined with numerical examples,the MATLAB software is used to calculate the curves of the elastic deformation of each driving and moving platform with the length of the drive rod.