In this paper, analytical and numerical solutions are developed for the pile with a rectangular cross-section under vertical load in layered soils. The rectangular cross-section is considered as a circular cross-section with a proposed formulation of equivalent radius. A number of bar elements models the pile and soil column below the pile tip while a series of independent springs distributed along the pile shaft with spring stiffness determined by properties of the corresponding soil layer models the surrounding soil. The method is based on energy principles and variational approach and the 1D finite element method is used in a pile displacement approximation. A new equation for modulus reduction appropriate for the rectangular pile is also developed to match the results of the proposed method to those of the three-dimensional (3D) finite element analyses. The proposed solution verified by comparing its results to the 3D finite element analyses and the comparisons are in excellent agreement. Keywords: rectangular piles; variational; energy principle; vertical load; finite element.