Using a two‐dimensional, three‐component MHD model in the heliospheric meridional plane, the propagation properties of transient shocks are investigated with emphasis on the influence of the heliospheric current sheet (HCS), the heliospheric plasma sheet (HPS) and the low‐speed stream on the shock propagation. The results show that the HCS and HPS have little effect on the shock propagation, whereas the low‐speed stream remarkably changes the shock propagation properties. The reflection of a shock against the low‐speed stream leads to a speed‐up and strengthening of the shock situated at the same side as the shock disturbance source. On the other hand, the resistance of the low‐speed stream against the shock transmission results in a delay and weakening of the shock situated at the opposite side to the shock disturbance source, but the shock front is widened in latitude. After the shock transmission, the low‐speed stream region is bent toward the shock propagation direction and disturbed, leading to complex fluctuations in the downstream of the shock. In the downstream of the shock on the opposite side to the shock disturbance source, the reflected wave interacts with the plasma there, and thus leads to the occurrence of complex fluctuations as well.