The mixed boundary problems for a mixed mode crack in a finite plate are studied. Based on the stress conditions of uniform loading on crack surfaces, a set of stress functions is proposed, which is also suitable for the case of crack surface without loading. The stress intensity factors (SIFs)are calculated by using the boundary collocation method. For mixed mode crack under resultant force boundary conditions, the present results agree very well with the existing solutions. For mixed mode crack under mixed boundary conditions, the SIFs have been obtained for different crack angles.