We investigate the effects of viscoelastic (VE) rheologies surrounding a vertically dipping prolate spheroid source during an active period of time-dependent deformation between 1995 and 2000 at Long Valley caldera. We model a rapid magmatic inflation episode and slip across the South Moat fault (SMF) in late 1997. We extend the spherical VE shell model of Newman et al. [Newman, A.V., Dixon, T.H., Ofoegbu, G., Dixon, J.E., 2001. Geodetic and seismic constraints on recent activity at Long Valley caldera, California: Evidence for viscoelastic rheology. J. Volcanol. Geotherm. Res. 105, 183–206.] to include a prolate spheroid geometry more accurately representing the probable source geometry inferred from other studies. This paper presents the first attempt to geodetically constrain the volcanic deformation source volume at Long Valley, a parameter for hazard assessment. Including fault slip along the SMF explains significant deformation observed with several EDM baselines and components of two continuous GPS time series. Additionally, the model explains the spatial extent of deformation observed by InSAR data covering the 1997–98 inflation episode. For the time period studied, the VE model requires modest pressure changes (maximum of 14.3 MPa) that are far lower than the overburden pressure (∼115 MPa), and less than the maximum for a purely elastic model with the same geometry and elastic strength (∼45 MPa). Thus, the inclusion of a realistic VE component significantly lowers the inferred pressures necessary to explain observed surface deformation. Though our model is non-unique, it is consistent with a broader variety of data compared to purely elastic models. Only right-lateral slip, and not dilitation, was necessary to explain offsets in EDM data near and crossing the SMF.