Closed-form solutions and their associated spreadsheet program (GASLFP) were developed by the first author for laterally loaded free- head piles in elastic-plastic media. The solutions show behaviour of a laterally loaded pile is dominated by net limiting force per unit length (LFP) fully mobilised along the pile to a depth called slip depth. They are characterised by three parameters of Ng, α o and n (to describe the LFP) and the soil shear modulus (Gs). Conversely, these parameters may be deduced by matching the predicted with measured response. To facilitate practical design, in this paper, the input values of Ng, α o, n and Gs were deduced in light of measured response of 20 piles tested in sand. The result allows effect of pile types, installation action, and dry or submerged sand to be clarified. In addition, using analogy to pipeline-soil interaction, a new alternative expression described by the parameters kp, α o and n is proposed to construct the LFP. The use of the previous parameter Ng and the new kp is discussed at length. Critical responses for typical deflection levels have also been provided. This back-analysis is elaborated via three typical cases.