In this study, the Stokes flow in the microchannel is analysed where the semicircular protuberances with constant spacing are attached on the upper and lower walls with staggered arrangement. For the low Reynolds number flow in microchannel, Stokes approximation is used and the periodicity and symmetry of the flow are considered to determine the stream function and pressure distribution in the flow field by using the method of least squared error. As results, the streamline patterns and pressure distributions in the flow field are shown for some specific values of the size and spacing of the protuberances, and shear stress distributions on the surface of semicircular protuberances are plotted. Especially, for an important physical property, the average pressure gradient along the microchannel is obtained and compared with that for the case of in-phase arrangement of the upper and lower protuberances. And, for the small clearance between the protuberances of upper and lower walls or between the protuberances and the opposite wall, the average pressure gradient is derived from the lubrication theory and compared with that of the present study.