Laterally loaded piles find wide application areas. Some of those application areas of laterally loaded piles are bridge foundations, ports and landslides. Accurate and simple calculation of lateral displacement of laterally loaded piles becomes vital for structure safety. Measured from the ground surface, the distance to the point on the pile where the deformation in the direction of the load (applied at the top of the pile) becomes zero is called the critical depth of pile. Laterally loaded pile faces with passive resistance in front of pile, active resistance at back side of pile and frictional resistance at sides of piles along pile critical length. In this study, pile properties, applied load and resistance forces pile faces are modeled in two-dimensional to determine lateral displacement of pile under lateral load using elasticity curve equations. The measured lateral displacements of three tested laterally loaded steel pipe piles are compared with both the analysis of equations proposed in this study and the analysis results of computer program LPile based on the p-y curves. It is found that the proposed equations to determine lateral displacement of laterally loaded steel piles in cohesionless soils yield to very close result of field measured lateral displacements.