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This thesis is concerned with the modelling of patient length of stay in public hospitals in Mexico. Patient length of stay is the most commonly worldwide employed outcome measure for hospital resource consumption and performance monitoring. Most of the hospitals around the world use average length of stay as starting point for resource planning. However average estimates frequently gives non-accurate results due to the high variability of the length of stay data. The reason for such high variability may be attributable to the diversity in the patient population and the environment where the patient is treated. Through a systematic review of the literature on methods and models in the field of calculating and predicting patient length of stay, this research highlights the areas of opportunity and research gap from previous studies and practices, and proposes the use of finite mixture models to approximate the distribution of length of stay. Also, these models are proposed as the foundation of more sophisticated models designed to include the internal and external factors associated with LoS. In this context, the thesis proposes three different approaches to explore such factors: individual-based approach, group-based approach and multilevel group-based approach. These interrelated approaches allow a better understanding of the diversity in the patient population and enable length of stay predictions for individual patients, and for cohorts of patients within and between hospitals. In addition, this research is built and evaluated using data from all types of patients treated at two public hospitals operating in Mexico. It is the consideration of the full case-mix of these healthcare facilities that gives this research its unique nature.