The influence of nonlocal effects has been investigated for the metallic nano chain constructed of Au cylinders straightly arranged in one direction. The chain has two-unique propagation modes, longitudinal and transverse ones, and our investigation for the nonlocal effects has been made especially in terms of those. Obtained results clarify the relationships between the influence of the effects and the arranged cylinders characterized by the smallness and adjacency which deeply affect to also the propagation property of the two modes.