Radiation forces exerted upon a dielectric, circular-shaped cylinder of infinite length illuminated by a non-paraxial cylindrical Gaussian beam are considered. Vectorial projections of the radiation pressure force on a dielectric, arbitrary- and circular-shaped cylinder are expressed analytically. In particular, the radiation force is expressed through coefficients of the decomposition of the non-paraxial Gaussian beam into the cylindrical functions. Using numerical examples, a possibility to optically trap a circular-shaped cylinder in a non-paraxial cylindrical Gaussian beam is demonstrated. (c) 2006 Optical Society of America.