Pile foundations supporting offshore structures are typically subjected to lateral cyclic loading. In design, the pile response under peak design load is generally estimated using a beam-column model where soil-structure interaction is simulated with a series of uncoupled non-linearly force-displacement springs (p-y curves) along the depth of the pile. In clay, the current state-of-practice uses p-y springs derived from some limited field pile tests carried out in the 1950s at Sabine River site, where only one soil type was tested and the cyclic load history applied in the tests was intended to provide a lower bound estimate of soil reaction under cyclic loading. In this study, comprehensive analyses are carried out to investigate the pile responses under two representative storm load histories (Gulf of Mexico (GoM) hurricannes and North Sea winter storms), in three different soil conditions (Gulf of Mexico clays, North Sea soft clays and North Sea stiff clays) for two types of structures (jackets and spars). The analyses use a numerical procedure that was developed in recent years and is fundamentally based on soil response measured at element level. From the parametric analyses, cyclic p-y curves are recommended for the design of jackets under GoM and North Sea metocean and soil conditions, and for spar anchors in GoM conditions.