Elastic-plastic, closed-form solutions were developed recently by the author, to capture the nonlinear response of laterally loaded rigid piles. Presented in compact form, the solutions are convenient to use, and sufficiently accurate despite using only two input parameters of the net limiting force per unit length pu along the pile, and a subgrade modulus k. Nevertheless, piles may be subjected to limited cap-restraints or loading below ground surface, which alter the response remarkably.This paper provides explicit expressions for estimating loading capacity of anchored piles and develops new solutions for lateral piles with cap-rotation by stipulating a constant pu or a linear increasing pu (Gibson pu) with depth. Lateral loading capacity Ho (at the tip-yield state and yield at rotation point state) and maximum bending moment Mm (at the tip-yield state) are presented against loading locations, and in form of the lateral capacity Ho-. Mo (applied moment) locus. The capacity is consistent with available solutions for anchored piles, and caissons with either pu profile, allowing a united approach from lateral piles to anchored piles. The new solutions are also presented in charts to highlight the impact of rotational stiffness of pile-cap on nonlinear response, offering a united approach for free-head piles through fixed-head piles.Several advantages of the solutions are identified against the prevalent p-. y curve based approach. To estimate the key parameter pu, values of the resistance factor Np (=ratio of pile-soil limiting resistance over the undrained shear strength su) are deduced using the current expressions against available normalised pile capacity involving the impact of gapping (between pile and soil), pile movement mode, pile slenderness ratio, inclined loading angle (anchored piles) and batter angles (lateral piles). The Np is characterised by: (i) An increase from 5.6-8.6 to 10.14-11.6, as gapping is eliminated around lateral piles and caissons, and from 1.0-6.1 to 2.8-9.8, as translation is converted into rotation mode of footings. (ii) Similar variations with slenderness ratio between anchors and caissons (without gapping), and among anchors, caissons and pipelines (with gapping). And (iii) A reduction with loading angles (anchors) resembling that with batter angles (piles). © 2013 Elsevier Ltd.