In this work different nonlinear hyperelastic models for slightly compressible materials are implemented in an isogeometric finite element model. This is done within the recently developed computational framework called PetIGA, which uses isoge- ometric analysis and modern computational tools to solve systems of equations directly and iteratively. A flexible theoretical background is described to implement other hyperelastic models and possibly transient problems in future work. Results show quadratic convergence of the nonlinear solution consistent with the Newton-Raphson method that was used. Finally, PetIGA proves to be a powerful and versatile tool to solve these types of problems efficiently.