To explore progressively larger biomolecular systems, methods to model explicit solvent cheaply are required. In this work, the use of Graphics Processing Units, found in commodity video cards, for solving the constraints, calculating the non-bonded forces and generating the pair list in the case of the fully constrained three site SPC water model is investigated. It was shown that the GPU implementation of the SPC constraint-solving algorithm SETTLE was overall 26% faster than a conventional implementation running on a Central Processing Unit (CPU) core. The non-bonded forces were calculated up to 17 times faster than using a CPU core. Using these two approaches, an overall speed up of around 4 times was found. The most successful implementation of the pair-list generation ran at 38% the speed of a conventional grid-based implementation on a CPU core. In each investigation the accuracy was shown to be sufficient using a variety of numerical and distributional tests. Thus, the use of GPUs as parallel processors for MD calculations is highly promising. Lastly, a method of calculating a constraint force analytically is presented.