This research addresses a two-dimensional stock cutting problem encountered at the New River Valley Workshop (NRV), Inc. in Radford, VA. This research considers recent literature on two-dimensional stock cutting techniques, pattern generating methods, solution approaches, and practical problem considerations in addressing the NRV cutting problem. Linear Programming analysis is applied to NRV's two-dimensional cutting problem. A computer-based implementation of the LP solution methodology is developed and used to solve NRV cutting problems. Test data and sample problems are used to demonstrate the efficiency, speed and accuracy of the computer-based system. Solution results from test data are compared to current NRV performance, illustrating the significant improvements in solution time and stock utilization that can be attained through the use of LP techniques and this computer-based implementation.