The flow problem within a straight microchannel of arbitrary cross section is analyzed. Exact analytical Solutions for flow profile of a channel flow with no-slip boundary conditions have been obtained ill literature only for simple geometry of channel section. In this paper. a number of problems with more complicated geometries arc solved either exactly or approximately. Three general solution methods are discussed, namely, complex function analysis, membrane vibration analogy and variational method. The usefulness of each method is justified with the help of examples. (C) 2008 Elsevier Ltd. All rights reserved.