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This study makes the first attempt to apply a recent strong-form boundary collocation method using the singular fundamental solutions, namely the singular boundary method (SBM), to 2D and 3D modified Helmholtz equations. By the desingularization of subtracting and adding-back technique, the corresponding nonsingular SBM formulations are derived based on null-field integral equations and an inverse interpolation technique. Numerical demonstrations show the feasibility and accuracy of the present SBM in some benchmark problems.