Ritz method was adopted to study the natural frequency of nonlocal elastic bar. Nonlocal elastic theory, different from classic elastic theory, was presented that the stress of a point is related to the strain of the area around the point, and such a relationship is illustrated by kernel function. Based on Eingen's nonlocal elastic model, a dynamics analysis of nonlocal elastic bar was created by Ritz method with three different kernel functions and the natural frequencies of the bar with two different boundary conditions were supplied. Compared with other methods, this one can deal with different kernel functions. Moreover, its numerical precision is controllable and programming is very convenient.