Loading of the Earth by the temporal redistribution of global atmospheric mass is likely to displace the positions of geodetic monuments by tens of millimeters both vertically and horizontally. Estimates of these displacements are determined by convolving National Meteorological Center (NMC) global values of atmospheric surface pressure with Farrell's elastic Green's functions. An analysis of the distances between radio telescopes determined by very long baseline interferometry (VLBI) between 1984 and 1992 reveals that in many of the cases studied there is a significant contribution to baseline length change due to atmospheric pressure loading. Our analysis covers intersite distances of between 1000 and 10,000 km and is restricted to those baselines measured more than 100 times. Accounting for the load effects (after first removing best fit slope) reduces the weighted root-mean-square (WRMS) scatter of the baseline length residuals on 11 of the 22 baselines investigated. The slight degradation observed in the WRMS scatter on the remaining baselines is largely consistent with the expected statistical fluctuations when a small correction is applied to a data set having a much larger random noise. The results from all baselines are consistent with ~60% of the computed pressure contribution being present in the VLBI length determinations. Site dependent coefficients determined by fitting local pressure to the theoretical radial displacement are found to reproduce the deformation caused by the regional pressure to within 25% for most inland sites. The coefficients are less reliable at near coastal and island stations.