A computer code TWOLASER has been developed for neutronic calculations of square lattice cells in nuclear power reactors. The computer code, which uses new methods for solutions of the integral transport equation and burnup equations, has been used to assess the accuracy and speed of the LASER code. The new code considers actual two-dimensional geometry of the cell as compared to the one-dimensional approximation used by LASER. Calculations have been performed on a sample problem for a burnup of 10.6 MWd/kg fissile. Results from these calculations show that the one-dimensional approximation used by LASER is good for the sample problem. However, the method used by LASER for the solution of burnup equations is not efficient. A modified version, MLASER, of the LASER code has also been developed in this research. This version uses the one-dimensional approximation of LASER and the new method for the solution of burnup equations, and it also provides good results as compared to the results given by the two-dimensional code. However, for the same accuracy, MLASER is computationally much faster (a factor of 4) than the original LASER program. The code TWOLASER can be used to provide data for benchmarking, and MLASER can be used for the replacement of the original LASER.