Surface displacements induced by ice load variation through time are calculated by spatial integration of Green's function for both end-members: an elastic half-space and a thick elastic plate lying over an inviscid mantle. The elastic half-space model allows the consideration of displacements caused by short-term (seasonal) variations. The thick plate model describes the final relaxed state. The transition between these two stages is dominated by an effective relaxation time which depends on mantle viscosity. This behaviour is considered to estimate displacements induced by long-term load changes (ice retreat over decades). We apply these methods to the Mýrdalsjökull ice cap, Iceland, where an annual cycle in ice load occurs as well as a gradual ice retreat as a consequence of climate warming. Seasonal vertical displacements measured from 2000 to 2006 at two continuous GPS stations located near the edge of Mýrdalsjökull ice cap fit well to a model of an elastic response to the annual variation in ice load. A comparison of model displacements and observations provides a minimum value of 29 ± 5 GPa for the effective static local value of the Young's modulus. We infer long-term displacements induced by ice retreat over the last 115 yr using a combination of the instantaneous elastic response and the final relaxed state. Results are compared to GPS measurements used to monitor the Katla volcano lying beneath the Mýrdalsjökull ice cap. A forward model considering an elastic thickness of 5 km can explain a fraction of the uplift recorded from 1999 to 2004, but it cannot account for the observed horizontal velocities. The study confirms that magma inflow is required to explain observed inflation of the Katla volcano 1999–2004.