Brachytherapy refers to the therapeutic use of encapsulated radionuclides within or close to a tumor. Today brachytherapy is used as an alternative to surgery or beam therapy to treat different kinds of cancers such as breast, lung, prostate, ovarian and pancreatic, primary and metastatic hepatic tumors and rheumatoid arthritis. Microspheres are one therapy utilized in brachytherapy procedures. Despite the development of advanced equipment and methods, there is still a limited knowledge of radiation dose distribution when utilizing this technique. This study focuses on random packing of microspheres and seeks to determine dose distributions for specific cases. The Monte Carlo Neutral Particle code (MCNP) developed by Los Alamos National Laboratory is used to simulate beta particle transport. Pr-142 is the beta source utilized for all calculations. The cylinder radii are 0.1, 0.15 and 0.3 cm and sphere radii are 0.03, 0.05 and 0.07 cm. The results are verified by examining limiting cases: uniformly distributed source and line of microspheres. Based on the data collected, the correlations between the average dose, its related variance, and distance from the cylinder were determined. An approach for estimating the surface average dose was developed and suggestions regarding an approach to assess surface variance estimation were presented.