In the present investigation an attempt has been made to solve the two-dimensional incompressible viscous flow past an impulsively started circular cylinder for Reynolds numbers ranging from 20 to 5000 using higher-order semicompact scheme (HOSC). Unlike conventional higher-order compact schemes the HOSC scheme has been developed to handle the circular geometry of the chosen problem and the intensive algebraic manipulations have been reduced considerably by relaxing the compactness of the computational stencil for few terms (but retained for most of the terms) of the discretized equations. For the flow past an impulsively started circular cylinder the results obtained at low and moderate Reynolds numbers have been validated with the experimental and numerical observations available in the literature. For high Reynolds number flows, the present scheme rightly captures the α phenomenon at Re=1000 and both β and α phenomena one after the other at Re=5000. © 2005 The American Physical Society.