Response of lateral pile groups is modeled using the more accurate (than any other numerical modeling) p − y curves-based load transfer model. It is essentially underpinned by limiting force per unit length pmpu, modulus of subgrade reaction pmk, and p-multiplier pm (to cater for pile-pile interaction, pm ¼ 1 for single piles). With the model, new closed-form solutions are developed incorporating the cap-rotational stiffness kr. The solutions are presented in nondimensional charts for free-head (kr ¼ 0) through fixed-head (kr > 10 times the pile bending stiffness). The study reveals that the existing pm (bearing no link to the stiffness kr) is inconsistent with pm ¼ 0.25 for capped piles (at limiting state of elastic solutions). This casts doubt about the accuracy of available solutions, and a compatible stiffness kr and pm is required. The compatible normalized stiffness knr is equal to 0.275-0.333 (n ¼ 0.7) and 0.333-0.564 (n ¼ 1.7) for the associated pm at the design level of (ground-level) bending moment specified in the JGJ code. Use of the solutions is elaborated for a typical offshore pile group against measured response, which largely substantiates the deduced stiffness knr. The coupled kr and pm revealed are fundamental to design of the capped piles using any methods. The new solutions using the knr and pm values should be employed to conduct pertinent design.