In this study, an inhomogeneous Cosserat rod theory is introduced and compared to the conventional homogeneous rod for modeling soft manipulators. The inhomogeneity is addressed by considering the pressure actuation as part of the rod's constitutive laws, resulting in shifting the neutral axis. This shift is investigated for a soft manipulator with three parallel fiber-reinforced actuators. Furthermore, a fiber-reinforced actuator is modeled using nonlinear continuum mechanics to extract the effect of radial pressure on axial deformation and is combined with Cosserat model. Finally, several numerical methods are employed to solve the proposed model and validated by a series of experiments.