A rigorous theory is developed to predict the radiation pressure force (RPF) exerted on a spheroid by an arbitrarily oriented and located shaped beam. Analytical expressions of RPF are derived for a homogeneous spheroid, which can be prolate or oblate, transparent or absorbing. Exemplifying calculations are performed and RPF calculations for spheroids are compared to RPF calculations for spheres. The "Optical Stretcher" is also numerically simulated to study the RPF exerted on a red blood cell during its deformation.