Traditionally, deglaciation-induced polar wander changes are modelled using a saw-tooth-shaped function for the time-history of ice sheets and spherical caps to express their spatial extent. In this contribution we present a set of analytical formulae that allow for a more realistic temporal evolution as well as spatial distribution of current ice masses and the corresponding sea level change when partly or completely melted. Starting with the linearized Liouville equations we develop closed-form time-domain solutions via the Laplace-domain, which are based on the assumption of a piecewise linear time-history of the perturbation of the inertia, which do not require the solution of convolution integrals. As being a central aspect of polar wander modelling we also revisit perturbation of the moment of inertia changes due to arbitrary surface loading due to changes in ice and ocean water masses and compare them with the result of the more simplistic models of spherical ice caps and a uniform sea level change. Finally, the correctness of the developed formulae is checked by various numerical checks based on more simplistic models and numerical integration techniques.