This thesis is divided into six chapters. The first chapter provides a brief introduction concerning the behaviour of brittle materials. It also contains the justification for the undertaking of the study as well as a brief description of the method of approach adopted, and thesis layout. Chapter two provides a critical review of the current literature available at present in the failure prediction brittle materials. Both theoretical and experimental studies are discussed and the relevance to the present work is justified. Chapter three deals with the numerical analyses adopted within the thesis. Five different failure criteria were utilized in the initial analysis of the results presented. Among them, the empirical model using the Principle of Independent Action satisfactorily represents the biaxial fracture behaviour of brittle materials in both tension-tension and tension-compression quadrants. Its validity has never been tested before. Various statistical fracture models were used to analyze the failure of brittle materials under multiaxial states of stress, the experimental failure data for simple tension being a starting point for their calculation. It was shown that the Energy Density theory led to a better agreement with the experiments than any other well-known fracture criterion. The study investigates methods of evaluating the Weibull parameters which were crucial in the failure prediction of brittle materials. Monte Carlo simulation techniques are also presented as a method of evaluating the data ranking for the failure probability of brittle materials. Chapter four is devoted to the description of experimental techniques adopted in the study, using specially designed rigs. Six different tests were conducted to evaluate the performance of brittle materials in static loading and also to enable comparisons with the theoretical predictions. Attention was given to specimen casting, loading frames, alignment, measurement techniques and other relevant parameters. The use of the linear elastic fracture mechanics method to predict the behaviour of cracks in bodies, which are subjected to steady stresses, is discussed. The compliance function for the three-point notch bend specimen is presented in addition to the determination of the fracture toughness of Herculite LX plaster. The work was also supplemented by the use of scanning electron microscopy (SEM) to failure analysis of plaster material. This is an extremely important tool in the study of brittle materials since the dimensions of small defects and fracture features on individual grains are often pertinent information to the failure analysis. Chapter five details the analysis of the theoretical results as well as the experimental findings. Based upon the previously mentioned approaches, a comparison was made between theoretically predicted and experimentally observed data. The comparison indicates that discrepancies exist between the observed and predicted results, the reasons for the discrepancies have been justified in this work. Chapter six provides a brief summary of conclusions derived from the complete study, together with recommendations for future work.