Flows past an inclined cylinder in the vicinity of a plane boundary are numerically investigated using direct numerical simulations. Parametric studies are carried out at the normal Reynolds number of 500, a fixed gap ratio of 0.8 and five inclination angles (α) ranging from 0° to 60° with an increment of 15°. Two distinct vortex-shedding modes are observed: parallel (α ≤ 15°) and oblique (α ≥ 30°) vortex shedding modes. The occurrence of the oblique vortex shedding is accompanied by the base pressure gradient along the cylinder span and the resultant axial flows near the cylinder’s base. The drag and lift coefficients decrease from the parallel mode to the oblique mode, owing to the intensified three-dimensionality of the wake flows and the phase difference in the vortex-shedding along the span. The Independent Principle (IP) is valid in predicting the hydrodynamic forces and the wake patterns when α ≤ 15°, and IP might produce unacceptable errors when α ≥ 30°. Compared to the mean drag force, the fluctuating lift force is more sensitive to the inclination angle. The IP validity range is substantially smaller than that for flows past a wall-free cylinder.