Using the representative volume element (RVE) method and finite element simulation, the stress and strain in the matrix of a fresh (0% fissions per initial metal atom burnup) UO2-Zr plate-type fuel were evaluated, considering both the periodic (ideal) and random dispersions of fissile particles. The histograms and descriptive statistics of Mises stress and the equivalent plastic strain in the matrix were computed and compared for both random and ideal distributions of particles. Our findings suggest that the random distribution of fissile particles has no considerable impact on the mechanical behavior of the zirconium matrix with respect to the ideal pattern. The plate performance related to the random distribution can be evaluated by examining descriptive statistics, such as the mean and standard deviation of the Mises stress, the cumulative probability of the average mean, and histograms of equivalent plastic strain and its distribution. These descriptive statistics can be utilized for the design of nuclear fuel plates; however, our study was limited by the assumptions and simplifications of the RVE and finite element calculations. Future work could include more realistic models, suitable failure criteria, and experimental validation.