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Abstract. Earth and other terrestrial and icy planetary bodies deform viscoelastically under various forces. Numerical modeling plays a critical role in understanding the nature of various dynamic deformation processes. This article introduces a newly developed open-source package, CitcomSVE-3.0, which efficiently solves the viscoelastic deformation of planetary bodies. Based on its predecessor, CitcomSVE-2.1, CitcomSVE-3.0 is updated to account for three-dimensional elastic compressibility and depth-dependent density, which are particularly important in modeling horizontal displacement for viscoelastic deformation. We benchmark CitcomSVE-3.0 against a semi-analytical code for two types of loading problems: (1) single harmonic loads on the surface or as a tidal force and (2) the glacial isostatic adjustment (GIA) problem with a realistic ice sheet loading history (ICE-6G_D) and an updated version of sea level equations. The benchmark results presented here demonstrate the accuracy and efficiency of this package. CitcomSVE-3.0 shows second-order accuracy in terms of spatial resolution. For typical GIA modeling with a 122 kyr glaciation–deglaciation history, a surface horizontal resolution of ∼50 km, and a time increment of 125 years, this takes ∼3 h on 384 CPU cores to complete, with displacement rate errors of less than 5 %.