The model-based forward and inverse problems in the diagnosis of structural crack location and size by using the finite element method of a B-spline wavelet on the interval (FEM BSWI) were studied. First the crack and uncracked elements of BSWI were built to solve the forward problem. The first three frequencies influencing functions of normalized crack location and size are approximated by means of surface-fitting techniques. Then the first three measured natural frequencies are employed as inputs of the functions. The intersection of the three frequencies contour lines predicted the normalized crack location and size. Both the numerical and experimental studies verified the validity of the BSWI elements in solving crack singular problems with high performance.