Sleepers are crucial for safety and comfort journey as static and dynamic loads are transmitted from railway vehicles to sleepers through rail. To reduce the maintenance cost and bear fatigue load, the demand for composite sleepers has been increased throughout the world. Generally, composite sleepers are comprised of recycled plastics, glass fiber, calcium carbonate/mica, polypropylene/high-density polyethylene, etc. Composites sleepers have a service life of at least 50 years and durability same as concrete without the weight or labor-intensive installation method. Ballast acts as elastic cushion between the sleeper and the subgrade supports the sleeper. The RDSO specifications for the Indian railways refer to the sleepers’ rigid fastening to the rails for the broad gauge. In the current study, static deformation and stress distribution due to load transmitted from the railway vehicle, dynamic analysis, and temperature distribution analysis have been done. The vertical displacement reaches its maximum value of 1.8 mm at the center of the sleeper and the Von Mises maximum stress value is 29.4 MPa. In this article, the fundamental frequencies and mode shapes of the sleeper's response under its own weight, free from any restraints, are determined by using ANSYS. Six different mode shapes are found in the frequency range 92–467 Hz.