We have performed a series of special very long baseline interferometry (VLBI) experiments that involve a significant fraction of group delay measurements made at very low elevation angles. Twenty-two such low-elevation experiments, each ∼26 hours in duration, were performed over a period of ∼2.5 years using VLBI antennas at the Goldstone complex in California and at Westford, Massachusetts. The purpose of these experiments was to expose and study errors in the formula for the elevation angle dependence of the atmospheric propagation delay, called the “mapping function.” Errors in this formula are a principal source of error in estimates of vertical coordinate of site position and make a significant contribution to the error in estimates of baseline length for transcontinental and longer baselines. For the low-elevation experiments, estimates of baseline length had a root-mean-square (RMS) residual about the mean value of 7 mm, or about 1.7 parts per billion for this 3900-km baseline. This scatter is about 20% greater than that calculated by propagating the random measurement noise through a Kaiman filter, which includes the noise contributions of the atmospheres and hydrogen maser “clocks” as well. We used specialized statistical tests to determine the contribution of mapping function errors to the estimates of vertical coordinate of site position and found this contribution to be less than 19 mm RMS. This value is roughly consistent with the observed larger-than-predicted scatter of the estimates of baseline length. We further found that for the 1–2 month spacing of our experiments, the mapping function errors do not exhibit a coherent annual signature but appear to be random in the long term.