Evaluation of residual strength of composite laminates with cutouts made in aircraft structures to accommodate piping or wiring create serious concern for the safety and reliability of the structure. Boron/epoxy laminates are used in aircraft and space vehicles for their high strength. Evaluation of stresses and residual strength of the laminate with square cutout are not analyzed in the literature. The present work is focused on studying the effect of orientation of square hole and fiber orientation on residual strength of the laminate and to suggest the best combination for higher residual strength. The analytical solution for stresses around holes in laminates is derived using Savins’s complex variables method to consider a multilayered plate with different hole shapes and orientations of loading. The residual strength of the laminate with hole is evaluated based on Tsai-Hill theory, Hashin-Rotem criterion and Tsai-Wu theory. The basic equations of failure criteria available for plain laminates are derived to calculate the residual strength of the laminates with hole using the stresses obtained from the analytical solution. The derived analytical solution is validated by reproducing exactly the same results of earlier researchers even by other formulations and also by the results of finite element analysis using ANSYS. The residual strength of the laminates with square hole is found to be dependent on orientation of hole as well as orientation of fibers and direction of loading and also on the degree of fiber matrix interfacial resistance. The values of failure strength are generally higher for square hole with normal sides for all cases laminates and loading. [0/90]s laminate with normal sided square hole gave consistently higher values of failure strength ranging from 11.4 to 18.2 MPa. Although [0/0]s laminate gives highest strength of 33 MPa for both normal and rotated orientations of the hole, it is not preferred due to highest stress concentrations at the corners that range between 12 to 37. Similarly, [45/-45]s laminate has its failure strength between 11.5 to 24.3 MPa, it is also not preferred due to its higher values of stress concentrations which range from 9.5 to 28. The analytical solution derived in the present work is the most general and unique as it can yield the stresses around any shape of hole and laminate geometry and all types of in plane loading. This solution will be able to reproduce the results of all other solutions available in the literature by different formulations.