A semi-analytical integral regularization algorithm is applied to the evaluation of nearly strongly-singular and nearly hypersingular surface integrals in the boundary element method (BEM) for three-dimensional potential problems.The algorithm is available for linear triangular isoparametric elements.The algorithm can be used to higher order elements by subdividing the element into triangular sub-elements.Due to singularity,the semi-analytical integral regularization algorithm is applied to the integral element close to the source point.The conventional Gauss quadrature is kept in the integral element far away from the inner point.The potentials and fluxes at the interior points close to the boundary are computed for three-dimensional heat conduction examples.The results demonstrate the accuracy and effectiveness of the algorithm.