Plot3D is the best for drawing functions defined on R2 (x-y) domain. Your cylinder is not such case.
You can use, e.g. :
ContourPlot3D[4 x^2 + y^2 == 16, {x, -2, 2}, {y, -4, 4}, {z, -2, 2}, BoxRatios -> Automatic]
Thank you VERY much. That helps a great deal!