In this paper, the elastostatic model of a novel hybrid robot for minimally invasive surgery is presented. The parallel robot has two identical limbs of SPU type and a RRR limb which allows the end-effector to accomplish spherical motion. The robot has three actuated joints for the parallel architecture and one for the translation along the longitudinal axis of the surgical instrument. The parallel manipulator provides remote centre of motion located at the incision point of the patient's body. First, the kinematics is solved in closed-form for the forward and inverse positioning problems, then elastostatic analysis of the parallel manipulator is modelled considering a system of flexible links and rigid bodies connected by means of joints. Local stiffness matrices are derived and finally combined to obtain the global stiffness matrix of the robotic system. Results are compared with those coming from commercial FE software for validation. Positioning and orienting errors due to flexibility are evaluated in order to improve quality in positioning and tracking of trajectories. Finally, some extensions to sensitivity analysis are provided to demonstrate that the elastostatic model can be used to improve the performance of the robot.