Postsynaptic calcium dynamics play a critical role in synaptic plasticity, but are often difficult to measure in experimental protocols due to their relatively fast rise and decay times, and the small spine dimensions. To circumvent these limitations, we propose to develop a computational model of calcium dynamics in the postsynaptic spine. This model integrates the main elements that participate in calcium concentration influx, efflux, diffusion and buffering. These consist of (i) spine geometry; (ii) calcium influx through NMDA receptors and voltage-dependent calcium channels (VDCC); (iii) calcium efflux with plasma membrane calcium pumps (PMCA) and sodium-calcium exchangers (NCX); (iv) intracellular calcium stores; and (v) calcium buffers. We herein present computational results we obtained and compare them with experimentally measured data, thereby validating the proposed model. Overall the development of such postsynaptic calcium model may help us better understand the intricacies of interplay between the different elements that shape calcium dynamics and impact synaptic plasticity in normal functions and pathologies. This model also constitutes a first step in the development of a nonlinear input-output calcium dynamics model for multi-scale, large scale neuronal simulations.