Percutaneous medical procedures rely upon clinicians performing precise needle insertion in soft tissue. The utility of haptic simulation systems in training clinicians for these procedures is highly dependent upon the ability to render accurate insertion force feedback. This paper presents a piecewise mathematical model for insertion force that does not require tissue material properties, detailed mechanical approximations, or complex computations. With manipulation of model parameters, a wide variety of insertion tasks and clinical scenarios can be modeled. Through needle insertion experiments and parameter estimation, this model was demonstrated to replicate the insertion forces associated with a variety of needle and tissue types. In 11 of 12 needle and tissue combinations tested, the model replicated the insertion force with an average absolute mean error of less than 0.065 N.