Direct numerical simulations are performed for the flow past an inclined square plate. The side length-thickness ratio of the plate is selected as 50, representing a reasonably thin plate. Various incidence angles of the plate with respect to the flow are considered from 0° to 75°, where 0° refers to the condition in which the flow is normal to the plate. The Reynolds number (Re) based on the flow velocity and the side length in the streamwise direction of the plate is up to 300. The hydrodynamic characteristics, including the force coefficients, the three-dimensional vortical structures and vortex shedding process, are presented. The effects of incidence angle on the wake transition are also discussed. It is observed that as the incidence angle increases, the flow firstly changes from a chaotic state to a periodic state and finally returns to chaos again at high incidence angles.