Modeling nonlinearities, including damage, in the boundary element method (BEM) is usually carried out in implicit way, or in other words via applying initial stresses or strains over a discretized domain part. Such initial values have no physical meaning. They are only used to compensate the stress level due to the occurred nonlinearity. In this paper explicit implementation of nonlocal damage is proposed. The damaged points inside the domain is physically weakened by decreasing their modulus of elasticity. With the help of Eshelby's equivalent inclusion theory, this idea is developed and implemented in this work. Load control solution algorithm is used. Both average strain and average damage nonlocal models are considered. Numerical examples are presented to verify the developed formulation. Factors that affect the solution accuracy are studied in details.