The modified mapping-collocation (MMC) method is applied to analyze a circumferential crack in an isotropic curved beam. Based on the method a MATLAB code was developed to obtain the stress field. Incorporating the stress correlation technique, the opening and sliding fracture mode stress intensity factors (SIF)s of the crack for the beam under pure bending moment load case are calculated. The MMC method aims to solve two-dimensional problems of linear elastic fracture mechanics (LEFM) by combining the power of analytic tools of complex analysis (Muskhelishvili formulation, conformal mapping, and extension arguments) with simplicity of applying the boundary collocation method as a numerical solution approach. Qualitatively, a good agreement between the computed stress contours and the fringe shapes obtained from the photoelastic experiment on a plexiglass specimen is observed. Quantitatively, the results are compared with that of ANSYS finite element analysis software. The effect of crack size, crack position and beam thickness variation on SIF values and mode mixity is investigated.