In this short report, we address the problem of constructing a right circular cylinder from a given set of ve 3D points. The idea is to be able to construct a cylinder in a similar way as one can construct a plane from three points, or a sphere from four points. This would be particularly useful for cylinder robust tting and cylinder extraction. However, this leads to a much more complex situation than for the plane or the sphere, since the equations involved are nonlinear with respect to the parameters. Our approach is to simplify the initial system of equations in order to get a more tractable computational problem. The system arrived at in this paper consists of three polynomial equations in three unknowns, of degree (2, 2, 3), which is simpler than the system found in related works. This system has been tested numerically using an interval analysis software.