Gantry Crane is also known as an overhead crane and widely used in industries, constructions or shipyards due to limited human capability to carry the various types of load. This system is developed to load and unload heavy materials from one place to another desired location. The problem is frequently occurs when the crane has to move the load at the required position while minimizing the sway angle of the oscillation. Thus, this research presents the investigation of the 2-D Gantry Crane System which focuses on the sway angle characteristics via Power Spectral Density (PSD) analysis. The mathematical dynamic model of the Gantry Crane System is developed using the Lagrange Equation. The system is simulated in MATLAB/Simulink environment and the results are presented in the form of time and frequency domain. A comparative assessment of the various payload mass and rope length of the system performance is presented and discussed.