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Large deformations and displacements of rock blocks may occur under high stresses around deep underground rock engineering works such as deep mines. The original discontinuous deformation analysis (DDA) developed by Shi and Goodman was dedicated to analyze large deformations, rotations and displacements of rock blocks by accumulating small components of these quantities in a time-marching scheme. The small rotation angle approximation adopted in the original DDA may induce block expansion with rotation (rotation error). Based on solid mechanics, the free expansion is caused by (1) the error due to the approximation of the real behavior using a displacement function, and (2) the theory used to describe the geometrical relationship between movement (displacement and rotation) and deformation. The original DDA uses the geometrical relationship that is based on small strain theory. Small strain theory assumes a linear relationship between displacement and strain that does not consider the high order components and the decomposition of rotation and displacement. The finite deformation theory, however, decomposes the displacement and rotation and gives a nonlinear relationship between displacement and strain. Therefore, the finite deformation theory can solve the block rotation problem at a higher accuracy. The DDA method is extended by coupling with the finite deformation theory. The implementation of this method is first verified by three illustration examples, and later employed to modelling a work face excavation of a coal mine in China. The stress field and displacement field are investigated. The results show that the occurrence of the first fracture of the key stratum increases the displacement and the stress. The second fracture of the key stratum partially releases the stress. The periodic weighting phenomenon is also reflected in this modelling. [ABSTRACT FROM AUTHOR]