In open channels, critical depth is an important aspect because it divides the two important flow regimes: sub-critical and super-critical flows. Critical depth is usually computed solving an implicit equation by tedious trial and error method. In this paper, a generalised numerical solution in the Chebyshev form to compute the critical depth is presented. The necessary parameters of some particular cases, namely rectangular, triangular, trapezoidal, circular and exponential channels, are furnished. The use of the Chebyshev approximation has the advantage requiring less iteration than any other iterative methods, such as Muller and Newton- Raphson approximations. © 2000 Taylor & Francis Group, LLC.