The effect of roughness on the wettability of an axisymmetric cylinder is investigated theoretically by making use of equilibrium meniscus shapes on solid surfaces analogously to previous studies for drops on horizontal surfaces. Employing circumferential sinusoidal and saw-toothed grooved structure, and using mechanistic arguments, one can explain wetting hysteresis, the formation of composite surfaces, and the presence of non-equilibrium jumps during contact line motion.On unidirectionally random surfaces the maximum surface slopes mainly determine the value of the advancing, and the minimum slopes of the receding contact angle. These effects of surface slopes diminish with decreasing roughness size. Diminishing roughness size also gives rise to numerous small non-equilibrium jumps imposed upon larger jumps during wetting. The contact angle hysteresis is found to show a nearly linear relationship with the spread in the distribution of solid surface slopes.