In order to investigate the shaping of aspherical planetary nebulae the gasdynamical conservation laws of mass, momentum and energy including radiation effects are solved numerically in twodimensional, spherical coordinates. The simulations describe the dynamical interaction of a fast, tenuous, spherically symmetric wind from the central star with the slow, dense, axisymmetric AGB-wind remnant and include photoionization, collisional ionization, collisional excitation, radiative recombination and forbidden line emission as radiation effects.