The nearly singular integrals occur in the boundaryelement analysis for the thin-wall structures and calculating thequantities at interior points close to the boundary. In this paper, thetriangular boundary element with three nodes is considered in thethree-dimensional boundary element analysis, where the relativedistance from a source point to the element is introduced to measurethe singularities of the integrals. The smaller the relative distanceis, the more difficult the integrals are to be evaluated. The surfaceintegrals on the triangular element are expressed in a local polarcoordinate system $\rho \theta $. Then the integrals are analyticallyintegrated with respect to the polar variable $\rho $ by means of theintegral formulae of some elementary functions. Thus the nearlysingular surface integrals are transformed into a series of lineintegrals along the contour of the element. The resulting lineintegrals are computed efficiently by the Gauss numerical quadratureinstead of the original singular surface integrals. Moreover, theregularization algorithm can also be applied to higher order elementsby subdividing the elements into several triangular sub-elements. Here,the algorithm is employed successfully to analyze the thin-walledstructures of the three-dimensional elasticity problems.