This work contains study of motion in the gravitational field of potential with central density peak and considers two models. We generalize spherical model to triaxial one using equipotential method. The values of structural parameters of models are chosen taking into consideration the condition of physical correctness (nonnegative density). We also analyze how structural parameters influence the orbits. Solving the Cauchy problem for system of differential equation different types of orbits for various initial conditions and parameters are constructed. We use symplectic methods of Euler and Nystrom as the system is hamiltonian. To increase the accuracy, we also used high-order methods as Merson and Dormand-Prinse methods.