Fixed bed reactor behavior as a function of inlet concentration, temperature and activity profile in the catalyst pellets was examined for the conditions proposed by INS, Pulawy. The results of the model calculations showed a good agreement with the experimental results. Two exothermic reactions (1) and (2) with kinetics described by Eqs. (3) and (4) are assumed to be carried out on catalyst pellets only in a heterogeneous tubular reactor. Mass and heat balances for the reactor are given by Eqs. (5) and (6) with initial conditions (7). Mass balance for the catalyst pellet is described by Eqs. (8) with boundary conditions (10)-(11). In the model described above the resistance of heat transfer from fluid to the catalyst pellet was neglected, because in the conditions investigated here preliminary calculations showed a very small influence of heat transfer resistance on the reactor behaviour. Moreover, heat balance for pellets has also been ignored, because the value of the parameter beta0, defined by Eq. (12), is equal about 5.10(-3), which suggests that the temperature of a catalyst pellet is constant. The system of equations (5), (6) and (8) has been rewritten in dimensionless form and solved using Euler method for the reactor heat and mass balance and the orthogonal collocation method for pellet mass balance. The dependence of various pellet activity profiles on the process selectivity (13) and conversion of acetylene E0 (14) for chosen values of the parameter epsilon0 (15) were investigated. The activity pellet profile was normalized according to Eq. (16). Uniform and shell (various thickness of the layer) profiles were investigated. Moreover, the temperature influence on the process selectivity and acetylene conversion for a chosen value of the layer thickness was considered. Figure 1 represents the selectivity and acetylene conversion in the reactor outlet vs. the thickness of the pellet active layer (X denotes the radius of inactive core of the pellet). Both the selectivity and coversion increase with decrease of the active shell width. The increase of the parameter E0 is accompanied by the increase of acetylene conversion but remarkable decrease of the process selectivity. Figure 2 shows the dependence of the selectivity and acetylene conversion on the position in the reactor. Selectivity decreases along the reactor axis the faster the parameter E0 increases. It is due to the increase of the ratio p(B)/p(A). Figure 3 represents the dependence of the selectivity and acetylene conversion on the inlet temperature in the reactor. The process selectivity and acetylene conversion first increase with increasing temperature and then decrease, but the inlet temperature area, where the process selectivity has the maximal value, is not the same values of conversion and vice versa. On the basis of calculations performed the following conclusions may be presented: 1. Using catalyst pellets with a narrow active layer on the outer part of the pellet is recommended. 2. The growth of hydrogen concentration at the reactor inlet improves the degree of acetylene conversion but, unfortunately, ethylene consumption is much greater. 3. The increase in inlet gas temperature is accompanied by the increase of acetylene conversion as well as ethylene consumption. 4. The results presented above show that it is possible to adjust the temperature and hydrogen concentration to optimize ethylene purification process.