Volcanic eruption rates in Iceland during the last deglaciation increased 5--30 fold from the steady-state rates. This has been understood by the unloading of ice, which increases the decompression rates in the mantle, causing enhanced mantle melting rates. However, existing theoretical work cannot account for large variations of Rare Earth Element (REE) concentrations in the Icelandic lavas. Lavas erupted during the last deglaciation are depleted in REEs by up to 70%; whereas, existing models can only produce at most 20% depletion. This dissertation attempts to find the causes of this mismatch and provides the first models that take account of the diachronous response of volcanism to deglaciation.

Numerical models of mantle flow and mantle melting response to the glaciation and deglaciation are developed. A time-lag sampler is incorporated to represent the time lag between the melt production at depths and the eruption on the Earth's surface due to finite rate of melt transport. The model results for the last deglaciation in Iceland show that the variations of REE concentrations are strongly dependent on the melt ascent velocity. This explains the REE concentration mismatch between the previous theoretical work and the observations. Comparison between the model results (timing of the bursts in volcanic eruptions, REE concentration variations, and volume proportions of the subglacial, finiglacial and postglacial eruptions) and the observational data suggests that the melt ascent velocity during the last deglaciation beneath Iceland is of the order of $\sim$100$\text{m/year}$.

The effects of glacial loading during the last glacial period on mantle melting are also investigated. It is found that glacial loading suppresses mantle melting and modulates the average REE concentrations in the melts due to the depth-dependent profile of mantle melting suppression. In addition, this dissertation explores how different deglaciation histories can result in different REE concentrations in the early-postglacial lavas. This may explain why lava shields formed during the Termination~II have different geochemical compositions from that formed during the Termination~I. Lastly, predictions for the future of the Icelandic volcanic eruption rates are made based on given estimated deglaciation rates of the current Icelandic glaciers.