Abstract We inverted 76 rates of change of baseline lengths measured with very long baseline interferometry (VLBI) during the period 1979–1989 to estimate the parameters of motions of the North American ( noam) and Eurasian ( eura) plates relative to the Pacific ( pcfc) plate. We considered two types of plate motion models, namely, rigid and non-rigid models. In the non-rigid models, we simultaneously determined the non-rigid motions of several stations near plate boundaries due to intraplate deformation. Intraplate deformation in the regions far away from plate boundaries is assumed to be negligible. Among several models considered, a non-rigid model called M2 is found to fit most closely to the observed data. In this model, six stations are assumed to be capable of the non-rigid motion; those are goldvenu, hatcreek, mojave12, ovro 130 and vndnberg, in the southwestern United States and kashima, in Japan. M2 gives parameter sets of 0.827 ± 0.035°/ m. y., about 50.5 ± 1.2° N, 78.5 ± 5.3° W and 0.889 ± 0.049°/ m. y., about 59.7 ± 1.9° N, 85.1 ± 7.4 ° W, representing the noam-pcfc and eura-pcfc relative motions. The plate motion parameters of M2 are nearly identical to those of the newest global-scale plate motion model nuvel-1. The noam-pcfc and eura-pcfc rotation rates of M2 respectively deviate only 0.044°/m.y. and 0.010°/m.y. from those of nuvel-1 (these deviations are only about 6% and 1%, respectively, of the rotation rates themselves). The noam-pcfc and eura-pcfc poles of M2 both lie only 2° from those of nuvel-1 (within a 2σ error ellipse of each pole). nuvel-1 is determined from spreading rates at mid-ocean ridges, azimuths of transform faults and earthquake slip vectors. Since the spreading rates are estimated from marine magnetic anomalies integrated over a geological timescale, nuvel-1 gives the plate motions averaged over this timescale. Thus, we may conclude that there is no appreciable difference between the plate motions averaged over a geological timescale (millions of years) and those in a recent short period ( ~ 10 yr). M2 also gives the horizontal non-rigid motions of VLBI stations in the southwestern United States at rates of 6–9 mm/yr and roughly in opposite direction to the rigid motion of each station associated with plate motion. hatcreek, located near the northern part of the Basin and Range Province (B&R), also shows additional westward motion of about 9 mm/yr, suggesting crustal stretching in the northern B&R. The US VLBI stations show subsidence at rates of about 5–7 mm/yr, except for goldvenu and ovro 130, whose subsidence is negligible. The Japanese VLBI station, kashima, has a horizontal non-rigid motion of about 20 mm/yr in the west-northwest direction, roughly opposite to the direction of the rigid motion. kashima also shows subsidence at a rate of about 12 mm/yr, which is larger than that deduced from geodetic data but consistent with the result from GPS.