In this paper, an isotropic elastic damage analysis is presented by using a meshless boundary element method (BEM) without internal cells. First, nonlinear boundary-domain integral equations are derived by using the fundamental solutions for undamaged, homogeneous, isotropic and linear elastic solids and the concept of normalized displacements, which results in boundary-domain integral equations without an involvement of the displacement gradients in the domain-integral. Then, the arising domain-integral due to the damage effects is converted into a boundary integral by approximating the normalized displacements in the domain-integral by a series of prescribed radial basis functions (RBF) and using the radial integration method (RIM). The damage variable used in the paper is the ratio of the damaged area to the total area of the material, and an exponential evolution equation for the damage variable is adopted. A numerical example is given to demonstrate the efficiency of the present meshless BEM.