Ordinary numerical computation methods (i.e., FEM and BEM etc.) lack the ability to present crack tip stress singularity, and meaningful procedures are required to determine stress intensity factors by use of the results from very near the crack tip. From this point of view, hybrid determination techniques are newly proposed to obtain reliable stress intensity factors with no special attention given to stress singularity. Crack tip stress and displacement behavior are expressed in the form of an infinite series expansion due to Williams and, usually, only the first terms of the series are considered when determining stress intensity factors (for example, extrapolation techniques). The hybrid determination techniques are based on considering the effect of including higher order terms, and results in solving simultaneous equations of the first degree derived by use of stress and displacement distributions. The characteristic of these techniques is that they are based on computation results from not very near the crack tip, and also that the higher order stress factors can be determined. These techniques are applied to BEM and FEM analyses of two dimensional and axisymmetric crack problems.