Early commercial PWR first cores started up without using burnable absorbers. This results in short first core cycle lengths, positive moderator temperature coefficients and high relative power peaking. Burnable absorbers are introduced to address these first core limitations. In the present work, the first part studies the effect of boron (as burnable poisons) concentration on a number of the small modular reactor assembly neutronic parameters. Among these parameters are the infinite multiplication factor, the depletion of U-235, the production of fissile plutonium isotopes (Pu-239+Pu-241), the total neutron flux, prompt neutron lifetime and effective fraction of delayed neutrons versus burnup. The effect of combination between soluble boron in moderator and gadolinium oxide mixed with uranium oxide is also investigated. For accomplishing this, MCNPX is used for modeling three small modular reactor assemblies. The first one is boron free model of enrichment 5% U-235. The other two assemblies use the same enrichment with soluble boron content 1000 and 2000 ppm respectively. The final conclusions of this part showed that the addition of soluble boron with moderator has a significant effect on the variation of K-inf versus burnup at the beginning and the end of cycle. Furthermore, the addition of soluble boron has an effect on the depletion of U-235. It is found that the weight percent of U-235 at 60 GWd/ton for the assemblies containing soluble boron is higher than that of the boron free assembly. For the mass of produced total fissile plutonium at the end of life, it is found that it increases for the models containing soluble boron. For fresh fuel, the effective fraction of delayed neutrons is directly proportional to the concentration of boron because of the higher content of U-235.The second part aims to study the effect of gadolinium enrichments and distributions on the reactivity of the assembly. Firstly, a comparison is carried out between non poisoned and poisoned assembly. Secondly, reactivity is studied for different models of SMR assemblies containing different numbers of gadolinium pins with (4% Gd2O3). Thirdly, reactivity and radial power distribution are analyzed for five different assemblies containing gadolinium rods of 12% Gd2O3. Using Gd2O3 for controlling excess reactivity and pin power peaking factor of the SMR fuel assembly has been also investigated. It was found that the five arrangements loaded with 88% UO2 and 12% Gd2O3 achieve a flat reactivity and radial power distribution. Therefore, these fashions could be used in the SMR core to guarantee the safe operation of the reactor. The results showed that a satisfactory value of the peaking factor is obtained at the beginning and the end of life for each assembly.