Capacity evaluation and planning usually relies on producing a closed queueing network model and predicting its performance indices. Until recently, analytical modelling of such networks was performed by using algorithms such as Convolution, RECAL or the Mean Value Analysis (MVA), prohibiting evaluation of systems offering multiple service classes to hundreds or thousands of users, a case commonly encountered in modern applications. Acknowledging this demand for performance evaluation, the Method of Moments (MoM) algorithm was introduced and addressed this problem. It was the first exact algorithm able to solve closed queueing networks with large population sizes. The MoM algorithm relies on the exact solution of large linear systems with integer coefficients of thousands of digits. The primary focus of this project is the production of an optimised implementation of the MoM algorithm as well as the algorithmic design, analysis and implementation of an exact parallel solver for linear systems it defines. Parallelisation is introduced in both algorithmic and implementation level by performing the operations over residue number systems and recombining the results by application of the Chinese Remainder Theorem. Various techniques have been introduced at all stages of this parallel solver to achieve improved time complexity and practical performance. Moreover, the procedure features several methods to achieve high robustness during error propagation when encountering a series of ill-conditioned linear systems which may be defined by the MoM implementation. Furthermore, a comprehensive test-set that corresponds to the requirements of modern application has been designed and is used to compare the performance of the different algorithms and configurations. Theoretical and experimental results regarding MoM and solver scalability are also presented. The overall result proved the improved performance of both the MoM algorithm over the established ones, namely Convolution and RECAL, and the parallel solver designed as part of this project over the serial one. The parallel MoM is the most efficient approach for evaluating models with several classes and queues and many hundreds of users. Lastly, much attention was paid in the efficient architecture and implementation design from a software engineering perspective, as the current implementation will be a part of the Java Modelling Tools (JMT) set of applications and may be augmented and improved in the future.