We study the model of a partially directed flexible or semi-flexible homopolymer on a square lattice, subject to an externally applied force, in a direction either parallel to, or perpendicular to the preferred direction. The polymer is self-interacting and can therefore undergo a collapse transition. We show that this model can be solved and we obtain the force-temperature phase diagrams which, for the case of flexible polymers, agree with that of Brak et al obtained using a different method. At sufficiently low temperatures, the polymer conformation changes from compact to coil state as the force is increased beyond a critical value. This transition is second or first order for the completely flexible or semi-flexible polymer, respectively.