The interaction between a shock-wave and the magnetopause is formulated on the basis of one-dimensional magnetohydrodynamics. The magnetopause is assumed to be a tangential discontinuity, and the magnetic field is limited to the case of perpendicularity. Both the forward and reverse shocks' impact on the magnetopause are considered and analyzed separately. The forward shock-magnetopause interaction results in a transmitted shock, a tangential discontinuity, and a simple rarefaction wave. The reverse shock-magnetopause interaction creates a transmitted shock, a tangential discontinuity, and a reflected wave. The propagation of an SSC signal which is related to an interplanetary shock-induced geomagnetic storm's onset-time on Earth is discussed in general terms. It was found in earlier work (Shen and Dryer, 1972) that the propagation velocity of an inter-planetary shock is decreased by about 10∼15% following its impact with the earth's bow shock; the present study shows that its velocity is then suddenly increased by a factor of two to three after impact with the magnetopause. The fast propagating shock-wave inside the magnetosphere degenerates into a hydromagnetic wave as it advances into an increasing intensity of the distorted dipole geomagnetic field.