Long-term forecasting, greater than a few hours, of geomagnetic activity requires reasonably accurate estimates of the arrival times of interplanetary shock waves of solar origin. The shock waves travel through an inhomogeneous interplanetary medium. Two major sources of uncertainty in estimates of arrival times are the variations of the velocity and the density of the ambient medium. The theory of propagation of strong shock waves through inhomogeneous media relates errors of estimate of shock arrival time to the inhomogeneities and shows that increases in the velocity along the Sun-Earth line lead to decreases in transit time and increases in the density lead to increases in transit time. The uncertainties in arrival time in both cases are proportional, in the linear approximation underlying the theory, to the perturbations or uncertainties in the velocity and density. The theory is applied to shock propagation through corotating inhomogeneities and used to calculate variances of arrival times using solar wind data. Four cases with di erent heliocentric radial dependences of density perturbation and ΓΏducial shock speeds are considered. Numerical results based on NSSDC OMNI data give a variance of about 12-24 h for a ΓΏducial transit time of 48 h, depending on the model for the inhomogeneities. In the most plausible model, in which the density inhomogeneities = increase linearly with heliocentric radius and the ΓΏducial shock speed is proportional to the inverse square root of the radius, the ratio of variance to transit time is about 0.25, independent of ΓΏducial transit time. The results are in general agreement with observations, suggesting that much of the variance of observed transit times results from the in uence of interplanetary inhomogeneities. Published by Elsevier Science Ltd.