Laser metal deposition is one of the most versatile methods in the expanding field of additive manufacturing. Its outstanding advantage is its capability to process a variety of metallic materials for the freeform fabrication of objects having sound mechanical properties. The process is used in applications of rapid manufacturing, components repair and surface coating. During recent years, modelling has been increasingly used to study and improve the laser metal deposition process. However, most models have focused on analysing individual stages of the deposition process and thus have not thoroughly dealt with the occurrence of mutually-influencing phenomena. This work presents a new numerical model that, starting from the simulation of powder particles in the deposition head, integrates the important phenomena and interactions that govern the dynamics of a powder stream and a deposition melt pool, within a single model for the first time.The resulting model is comprehensive enough to allow the prediction of the morphology of deposited tracks and structures and the heat flows during their creation; as well as the flexibility to simulate, in principle, any deposition shape. The model has been demonstrated using the settings of an actual laser metal deposition system, and has been applied to study clad formation in the deposition of single tracks, layers, walls and simple three-dimensional structures. Moreover, the model has been used to study the formation of irregularities and excessive mass deposition. A new sensor-less deposition control technique based on the simulation and testing of different deposition strategies prior to actual deposition, is proposed. As a demonstration of this control technique, the model has also been used to study the case where excessive deposition develops at intersecting or cornered tracks. Improved deposition strategies have been tested using the model and applied to real deposits. A two fold improvement in layer height control has been achieved in the case of cornered layers.The outcome of the work presented in this thesis can be applied in further studies and prediction of laser deposited shapes for real applications. Furthermore, it can be potentially used for improvement of the laser metal deposition technology through the simulation of deposition strategies prior to actual processing.