In this study we carry out the one-dimensional hybrid particle simulations of shock waves and discontinuities. The shock waves and discontinuities are generated in the plasma current sheet by means of the Riemann problem. The effects of pressure anisotropy and plasma beta on the discontinuity properties are examined. According to the Magnetohydrodynamics theory, slow shocks may become anomalous in anisotropic plasmas. The simulation results of this study show that the anomalies slow shocks may be generated in the kinetic simulations with initial temperature anisotropy. In particular, slow shocks with upstream wavetrains or moving ahead of rotational discontinuity may form for certain parameter regimes.