Myxobacteria are social bacteria that are remarkable for their complex life cycle. In vegetative state, when nutrients are available, myxobacteria cooperatively swarm on a solid surface and feed. When exposed to starvation conditions, myxobacteria exhibit multicellular morphogenesis: 10^5-10^6 cells aggregate to form a fruiting body. Due to their unique life cycle, myxobacteria often serve as relatively simple model organism to study multicellular development and morphogenesis. Myxobacteria cells glide on a substratum, periodically reversing direction and interact with surrounding cells of a swarm. During developmental process, myxobacteria cells often form various patterns: clusters of cells, domains of aligned cells, circular aggregates and streams of cells traveling into the aggregates. The goal of the thesis was to formulate a computationally efficient mechanical mass-spring model of a myxobacterium cell and study the importance of mechanical interactions between cells for the pattern formation in myxobacteria populations. In Chapter 2, a basic model was formulated and it was investigated how cell flexibility affects cell alignment in the population in two-dimensions. The model was formulated in terms of experimentally measurable mechanical parameters, such as engine force, bending stiffness, and drag coefficient. It was shown, that a population of rigid cells can align well due to mechanical interactions between cells, but that cell flexibility impedes the alignment. Theoretical estimations of cell flexibility suggest that myxobacteria cells could be too flexible for the population to align due to mechanical interactions. Therefore, in Chapter 3 lateral restriction of cell movement due to contact with the substratum was introduced in the model. It was shown that lateral restriction can increase the ability of a population of flexible cells to align. In Chapter 4 it was studied how reversal period of cells affects population movement patterns. The results indicate that short reversal period results in domains of aligned cells, whereas long reversal period produces cell clusters. Furthermore, the model reveals that in densely packed populations, non-reversing cells can sort themselves due to mechanical interactions to produce streams of cells that travel in the same direction. Chapter 5 introduces short-range guidance forces between the trailing pole of one myxobacterium and the leading pole of another and investigates the resulting patterns. It is shown that certain types of short-range guiding interactions can explain the formation of circular aggregates. In Chapter 6, the model is extended to three-dimensions and simulation outcome is compared with the results obtained in the previous chapters. The three-dimensional model shows that guiding interactions as in Chapter 5 can initiate the formation of unstable mounds. Finally, the thesis Outlook discusses a series of directions in which the current model can be extended to further understand the importance of mechanical interactions between gliding cells on the development of myxobacteria.