The characteristics of different types of the weighted functions are discussed, and the dependency of the influence domain on the intrinsic length scale is examined. Distribution of stress field of I-II mixed mode crack is analyzed by non-local theory with different types of weighted functions. The effects of the stress intensity factor KI and KII on the all components of strains at the crack tip are analyzed by the non-local theories based on different types of weighted functions. The non-local strain will be considerably reduced. The size of non-local strain field with the bell-shaped weighted functions is larger than that obtained by either Green’s or Gaussian weighted functions. The non-local theory is instructive to avoid the trouble resulting from stress singularity at crack tip.