A model of diffuse gamma-ray emission is presented. The diffuse gamma-ray emission is directly related to the distribution of gas and radiation in an object and to its star formation. The relationship with star formation is due to supernovae behaving as cosmic-ray accelerators. To model this emission from M31, I have used the HI map of Brinks & Shane (1984) to represent the atomic gas content and the CO map of Nieten et al (2006) to represent the molecular hydrogen content. To represent the radiation field, I have used maps of M31 in different bands, from infrared to ultraviolet. These images have been normalized to the spectral energy distribution of M31. The cosmic-ray spectrum is a power law whose indices are p = 2.76 for electrons and k = 2.71 for protons; heavier nuclei are not currently included. These two spectra have been normalized assuming energy equipartition between cosmic-rays and the magnetic field and a protonto- electron ratio of 100. In these calculations I used the values for the magnetic field strength given by Beck (1981) of 3.2 ± 0.9μG in the ring and 2.4μG in the disk. The gamma-ray mechanisms that are used in this model are neutral pion decay, bremsstrahlung and inverse Compton scattering. Production functions that express the number of gamma-rays produced per unit of time per unit of nucleon energy were obtained from Berstch et al (1993) and Haung et al (2007). The model uses maps of gas derived from HI and CO emission lines, and maps of the radiation field, and production functions as inputs. This gives a map of emission in gamma-rays of M31. The integrated flux above photon energies of 100MeV is 2.11 × 10−8 photon s−1cm−2. A maximum likelihood analysis was applied to the model map and the all-sky maps observed by EGRET. With this analysis I found an upper limit of 7.9×10−9photons cm−2s−1 to the gamma-ray flux above 100MeV for M31, implying a modification of the input parameters to the model. The most probable error in the input was adopting a magnetic field strength a factor of ∼ 2 too high. A field strength of ∼ 2μG is the most appropriate value on large scales in M31. The results of this model have been compared with flux estimates of M31 in the same energy range made by other authors. ¨Ozel & Berkhuijsen (1987) estimated a flux of 2.4×10−8ξ photons cm−2s−1 with ξ < 5 and Pavlidou & Fields (2001) calculated 1×10−8photons cm−2s−1 respectively.