Interfacial shear strengths or static frictions between carbon nanotubes (CNT) in contact at different cross angles are studied by using atomic mechanics. It is shown that the axial interfacial shear strengths between parallel CNTs in commensurate are two orders of magnitude greater than those in incommensurate. This strong chiral dependence is not surprising and is similar to that of the friction between two graphite basal planes. In contrast, we find that the interfacial shear strengths of crossly contacted CNT pairs are much less dependent upon chirality. The estimated values of interfacial shear strengths, ranging from 0.05 to 0.35 GPa, agree very well with experimentally measured results available in the literature. These results may thus be used as a basis for explaining the observed tension strengths of CNT bundles and films that are mainly bonded by van der Waals interactions and the mechanical behaviors of composite materials with highly concentrated CNTs.