Understanding the mechanical properties of diaphragms is crucial for the reliability and performance of Nano Electro Mechanical Sensors (NEMS). There are various methods documented for characterizing micro materials. One well-established nondestructive approach is the bulge test, which is effective for examining the mechanical traits of diaphragms. This study aims to enhance NEMS performance by exploring how a Nano rectangular diaphragm (NRD), created from a new material within NEMS, behaves mechanically through an improved bulge test technique. The NRD is made from layers of basalt fiber reinforced polymer (BFRP) laminate composites, sized at the nanoscale, and was tested at room temperature for plane-strain bulging. Before applying any loads, the NRD is pre-stressed to eliminate any initial deflection and then securely clamped between two plates. A differential pressure is applied, causing deformation in the laminated composite NRD. This setup makes the plane-strain bulge test well-suited for analyzing the mechanical properties of the laminated composite NRD in both elastic and plastic states. We derived an exact solution to the governing equations for the symmetric cross-ply BFRP laminated composite NRD, taking into account the impact of residual strength from the pre-stressed condition. The relationship between stress and strain for the BFRP laminated composite NRD was determined through hydraulic bulging tests, and we analyzed the gradual thickness changes at different points of the hemisphere formed during the bulge test. We can also extend a finite element model (FEM) to analyze the BT outcomes and look into how pre-stress influences the pressure testing, comparing results from the FEM with those derived from analytical calculations. The relative error (E_r) for w_max between the analytical and numerical results is less than 0.336%. We ran simulations using ANSYS, MATLAB and its PDE toolbox to get our results.