Some examples of plotting parametric surfaces with Mathematica: a cylinder and a torus.

ParametricPlot3D[ { Cos[u], Sin[u], v}, {u,0,2*Pi}, {v,0,2} ]

ParametricPlot3D[ {(2+Cos[u])*Cos[v], (2+Cos[u])*Sin[v], Sin[u]}, {u, 0, 2*Pi}, {v,0,2*Pi}]