We use numerical simulations to investigate whether Fermi first order acceleration can occur in oblique shocks. This process involves repeated shock-crossings by non-thermal particles and requires a mechanism by which particles that have crossed the shock can be reflected back towards it. Using the particle-in-cell (PIC) method, we follow the formation of the shock and determine the fraction of the particles that gets reflected into the upstream medium. Then, with this result, we use a combined PIC-MHD method to model the large-scale structure of the plasma and the magnetic field surrounding the shock and find out whether the reflected particles can trigger the instabilities in the upstream magnetic field that are required to reflect the particles back toward the shock. We find that the feasibility of this process in oblique shocks depends strongly on the Alfvenic Mach number, with higher Mach shocks being more likely to trigger the diffusive shock acceleration process.