Redistribution of air masses due to atmospheric circulation causes loading deformation of the Earth's crust, which can be as large as 20 mm for the vertical component and 3 mm for horizontal components. Rigorous computation of site displacements caused by pressure loading requires knowledge of the surface pressure field over the entire Earth surface. A procedure for computing three-dimensional displacements of geodetic sites of interest using a 6 hourly pressure field from the National Centers for Environmental Prediction numerical weather models and the Ponte and Ray  model of atmospheric tides is presented. We investigated possible error sources and found that the errors of our pressure loading time series are below the 15% level. We validated our model by estimating the admittance factors of the pressure loading time series using a data set of 3.5 million very long baseline interferometry observations from 1980 to 2002. The admittance factors averaged over all sites are 0.95 ± 0.02 for the vertical displacement and 1.00 ± 0.07 for the horizontal displacements. For the first time, horizontal displacements caused by atmospheric pressure loading have been detected. The closeness of these admittance factors to unity allows us to conclude that on average, our model quantitatively agrees with the observations within the error budget of the model. At the same time we found that the model is not accurate for several stations that are near a coast or in mountain regions. We conclude that our model is suitable for routine data reduction of space geodesy observations.