Morison's equation is used for formulating forces and moments due to waves acting on circular cylinders of varying cross-sections and truncated forms. First, the usual case of bottom-mounted constant-diameter circular piles extending from seabed to free surface is revisited and then forces and moments for the truncated form are formulated. Further, linearly and parabolically varying diameter cases are considered for both bottom-mounted and truncated cylinders. The formulations are derived using linear wave theory; however, by adopting a heuristic nonlinear approach integrals are evaluated from pile bottom to wave crest instead of still water level. Corresponding linear formulations are obtained as special cases by simply setting the non-dimensional nonlinearity parameters to zero. Thus, for each cylinder configuration two different force and moment formulas are presented by integrating to actual free surface and to still water level. All the results are arranged in forms which are practically easy to use. Finally, analytical expressions for determining maximum total force and moment values are given and sample calculations are presented for all configuration types.