We discuss the prospects for using very long interferometry (VLBI) to measure vertical crustal motions. Our analysis of this problem indicates that the main limitations of such VLBI measurements will probably arise from errors in modeling of the propagation delay through the earth's neutral atmosphere and errors in determining the orientation of a ''crust fixed'' coordinate system in the VLBI (intertial) reference frame. We examine two techniques for assessing the presision of vertical position measurements which can be made with currently available VLBI systems: (1) the repeatability of baseline length mesurements, and (2) the repeatability of the vertical site position of one site in a four-site network when the positions of the other three sites determine the earth orientation parameters. The repeatability of baseline length measurements implies that the precision of the vertical position estimates is ~8 cm, averaged over 13 sites (separated by 600--8000 km) and 4.5 years of data. The repeatability of vertical position estimates for the Richmond, Florida, site is ~7 cm for the 42 observing sessions carried out during an 11-month period. Both of the techniques we have used to estimate the precision of height determinations indicate that the current precision is ~8cm for a single 24-hour VLBI observing session. The effects of errors in the earth orientation parameters will depend on the distances between the VLBI sites and could induce errors as large as the precision given above.