The redistribution of past and present ice and ocean loading on Earth's surface causes solid Earth deformation and geoid changes, known as glacial isostatic adjustment. The deformation is controlled by elastic and viscous material parameters, which are inhomogeneous in the Earth. We present a new viscoelastic solid Earth deformation model in ASPECT (Advanced Solver for Problems in Earth's ConvecTion): a modern, massively parallel, open-source finite element code originally designed to simulate convection in the Earth's mantle. We show the performance of solid Earth deformation in ASPECT and compare solutions to TABOO, a semianalytical code, and Abaqus, a commercial finite element code. The maximum deformation and deformation rates using ASPECT agree within 2.6% for the average percentage difference with TABOO and Abaqus on glacial cycle (∼100 kyr) and contemporary ice melt (∼100 years) timescales. This gives confidence in the performance of our new solid Earth deformation model. We also demonstrate the computational efficiency of using adaptively refined meshes, which is a great advantage for solid Earth deformation modeling. Furthermore, we demonstrate the model performance in the presence of lateral viscosity variations in the upper mantle and report on parallel scalability of the code. This benchmarked code can now be used to investigate regional solid Earth deformation rates from ice age and contemporary ice melt. This is especially interesting for low-viscosity regions in the upper mantle beneath Antarctica and Greenland, where it is not fully understood how ice age and contemporary ice melting contribute to geodetic measurements of solid Earth deformation.