The increasing turbine sizes have necessitated monopiles in soft clay to have larger diameter and rigidity, from early design of flexible piles to recent semi-rigid piles, with future anticipating rigid piles. Existing few cyclic soil–pile interaction models are developed for flexible pile associated with full-flow failure (above the rotation point, RP), with little attention paid to semi-rigid and rigid piles involving rotational-shear failure (below RP). This study aims to unify the description of piles with varying rigidity by proposing a cyclic two-spring model, where lateral resistances above and below RP are described with cyclic p–y and M– θ springs, respectively. It naturally recovers to a cyclic p–y model for flexible piles. The cyclic p–y and M– θ formulations are developed within the bounding-surface plasticity framework, based on numerical results of cyclic soil–pile interaction concerning full-flow and rotational-shear mechanisms, respectively. These numerical analyses are performed using a cyclic plasticity clay model developed and implemented numerically in this study. The cyclic “ p–y+M– θ” model quantitatively reproduces experimental results of cyclic shakedown and ratcheting for flexible, semi-rigid, and rigid piles. Ignorance of the M–θ spring could underestimate cyclic resistance of rigid piles by 25%, suggesting the model’s merit in reducing conservatism for monopiles in feature designs.