General analytical solutions are given by means of Chebyshev polynomial for directional couplers, which are made up by lossless multi waveguides in a line or in a ring, weak coupling existing only between neighbored waveguides and polarization coupling being not considered also. As examples, expressions for the 2×2,3×3 and 4×4 directional couplers in the form of line are deduced. Besides, solution to the 3×3 directional coupler arranged in a ring is given and analyzed in detail.