We perform Monte Carlo (MC) and molecular dynamics (MD) simulations to study the adsorption and diffusion properties of methane and CO2 in cross-linked polyethylene in the temperature range 300-600 K. A hybrid MC/MD approach was used to incorporate the effects of framework flexibility and polymer swelling on the gas adsorption. The polymers show negligible swelling at the studied conditions. A nonmonotonic behavior of gas adsorption as a function of the cross-linking degree was obtained. Notably, a similar behavior was observed for the void fraction and pore diameters. This shows a direct correlation between gas adsorption and the pore characteristics of the cross-linked polymer network. Mobility of methane and carbon dioxide in the polymer matrix increases with temperature. Also, gas mobility decreases with increasing cross-linking degree, consistent with experiments. These results can be explained by the fact that the waiting time for a gas molecule in a cavity before the jump increases with decreasing temperature and increasing cross-linking degree. Interestingly, the activation energy for gas diffusion generally decreases with increasing cross-linking. This is possibly due to the fact that increasing the cross-linking degree leads to smaller pore sizes especially at high temperatures. Such a molecular-level understanding of adsorption and diffusion of gases in cross-linked polyethylene is important in improving the performance of polymer networks for potential applications in gas separation, barrier technology, and food packaging.