The author has studied the laminar flow in a meandering channel on the assumption that the curvature of the centreline is both small and slowly varying. Solution is obtained up to fourth approximation for a general shape of centerline using only elementary functions. However higher order approximations are necessary to go into the question of convergence of the series solution. The use of computer is essential for such higher approximations. Even though curved channel flow was studied up to second approximation earlier by \textit{C.-Y. Wang} [see J. Appl. Mech. 47, 7-10 (1980; Zbl 0437.76100)], only small variations in curvature are considered with small Reynolds number and not slowly varying curvature as is done in this paper. Wang's solution can be recovered for the second approximation from the present solution as a particular case for the annulus. The question of separation in a smoothly meandering channel of constant width is not as evident as it is for the symmetric channel.