Abstract: The details of the spectral element method are presentted. Then flow past two tandem circular cylinders at the Reynolds number Re=200 and four square-arranged circular cylinders with various spacing ratios at Re=150 are numerically investigated. We focus on the effects of spacing ratios L/D (ratio of center-to-center distance to diameter of cylinder) for the two cases above. The flow patterns, mean drag and lift coefficients as well as the Strouhal numbers are plotted as a function of the spacing ratio. The results reveal that the spacing ratio has a great impact on the flow characteristics of both the two-cylinder and four-cylinder cases. There is a critical spacing ratio of around 3.6 at Re=200 for the case of two tandem cylinders. Three different flow patterns are observed in the case of four-cylinders. Among different flow patterns, a transformation from one pattern to another will change the drag/lift forces and vortex shedding frequencies. The key mechanical parameters jump suddenly in some critical spacing ratio intervals.