In this paper, limiting force profile for laterally loaded rigid piles in sand and is differentiated from the on-pile force profile, from which elastic-plastic solutions are established and presented in explicity expressioins. Nonlinear responses of the piles are characterized by slip depths mobilized from mudline and the pile-tip. At the states of tip-yield and rotation point yield, expressions for some critical depths are developed, which allow the on-pile force profiles to be constructed. The solutions and the expressions are developed concerning a constant subgrade modulus (k) and a linearly incresing modulus with depth (Gibson k), respectively. capitalized on three measurable responses are presented for typical eccentricities from elastic state right up to failure. Comments are made regarding displacement-based capacity. A case study is elaborated to illustrate (i) the use of the current solutions; (ii) the impact of the k distrubutions, (iii) the evaluation of stresses on pile surface; and (iv) the deduction of soil modulus. The current solutions are easily implemented and suitable for general design.