Parallel computing has recently appeared has an alternative approach to increase computing performance. In the world of engineering and scientific computing the efficient use of parallel computers is dependent on the availability of methodologies capable of exploiting the new computing environment. The research presented here focused on a modeling approach, known as cellular automata (CA), which is characterized by a high degree of parallelism and is thus well suited to implementation on parallel processors. The inherent degree of parallelism also exhibited by the random-walk particle method provided a suitable basis for the development of a CA water quality model. The random-walk particle method was successfully represented using an approach based on CA. The CA approach requires the definition of transition rules, with each rule representing a water quality process. The basic water quality processes of interest in this research were advection, dispersion, and first-order decay. Due to the discrete nature of CA, the rule for advection introduces considerable numerical dispersion. However, the magnitude of this numerical dispersion can be minimized by proper selection of model parameters, namely the size of the cells and the time step. Similarly, the rule for dispersion is also affected by numerical dispersion. But, contrary to advection, a procedure was developed that eliminates significant numerical dispersion associated with the dispersion rule. For first-order decay a rule was derived which describes the decay process without the limitations of a similar approach previously reported in the literature. The rules developed for advection, dispersion, and decay, due to their independence, are well suited to implementation using a time-splitting approach. Through validation of the CA methodology as an integrated water quality model, the methodology was shown to adequately simulate one and two-dimensional, single and multiple constituent, steady state and transient, and spatially invariant and variant systems. The CA results show a good agreement with corresponding results for differential equation based models. The CA model was found to be simpler to understand and implement than the traditional numerical models. The CA model was easily implemented on a MIMD distributed memory parallel computer (Intel Paragon). However, poor performance was obtained.