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This work presents a regularized eigenstrain formulation around the slip plane of dislocations and the resultant non-singular solutions for various dislocation configurations. Moreover, we derive the generalized Eshelby stress tensor of the configurational force theory in the context of the proposed dislocation model. Based on the non-singular finite element solutions and the generalized configurational force formulation, we calculate the driving force on dislocations of various configurations, including single edge/screw dislocation, dislocation loop, interaction between a vacancy dislocation loop and an edge dislocation, as well as a dislocation cluster. The non-singular solutions and the driving force results are well benchmarked for different cases. The proposed formulation and the numerical scheme can be applied to any general dislocation configuration with complex geometry and loading conditions.