The propagation of shock waves in the solar wind and their three-dimensional interaction with the terrestrial bow shock, magnetosheath, and magnetopause is examined theoretically and compared with observations made by the ISEE spacecraft. First the formulae underlying the new position and orientation of the bow shock front after the interaction are given. Then magnetic field and plasma data from the ISEE 1, 2, and 3 spacecraft are compared with the theoretical estimates of the propagation time of the shock waves between ISEE 1 and 3. Examination of data obtained on August 18, 1978, when both ISEE 1 and 3 were in the solar wind, show good agreement with theory. Using a simple model of the magnetosheath, we can extend our predictions to include the propagation time through the magnetosheath. Two examples of the interplanetary shock interaction with the magnetosphere while ISEE 1 and 2 were in the outer magnetosphere on August 27 and October 4, 1978, show quite satisfactory agreement with the predictions of this simple model. On August 27, 1978, the magnetopause is blown well past ISEE 1 and 2, and the two spacecraft pass completely through the magnetosheath in 2.5 min. Rapid as this may appear, we show that this behavior is as predicted by the theoretical treatment.