A lot of researches have beendone to increase production of heavy oil and improve EOR methods, Because of increasing global oil demand, declining production of light oil reservoirs and increasing oil prices in recent years. Fractured hydrocarbon reservoirs are more than 20 percent of the world’s oil reservoirs so researchers are examining fractured reservoirs for more oil production. There are several mechanisms for crude oil recovery from the fractured reservoirs that the Spontaneous imbibition of water into the matrix blocks is the most important mechanism for reservoirs with low permeability. This project presented a numerical modeling of spontaneous imbibition process when water was imbibed by capillary forces into an oil saturated cube core for studying effect of capillary forces, oil and water relative permeabilities and viscosity. In this modeling, we assumed that imbibition process was a diffusion process, gravity forces were neglectedand capillary diffusivity coefficient (CDC) was a function of water saturation. Finite difference implicit method was used to solve the spontaneous and counter-current imbibition equations and finally imbibition process was simulated using MATLAB program. Accuracy of the modeling was investigated with comparison of the modeling results and the experimental data. After validation,the proposed model was used for studying the effect of capillary pressure, water and oil relative permeabilities and viscosity on the oil recovery. In order to examine the effect of capillary pressure, three different capillary pressures were used with multiplication in order of 0.1, 1 and 10 to the matching result of capillary pressure. Capillary pressure was driving force in the spontaneous imbibition process, thus, oil recovery was increased with increasing the capillary pressure.In order to examine the effect of relative permeability on oil recovery, three cases of oil and water relative permeabilities curves were used. Oil recovery was increased with increasing the oil and water permeabilities significantly but the effect of oil permeability was less. In order to examine the effect of viscosity, the oil recover curves for three different oil viscosities and three different water viscosities were plotted. Oil recovery was increased with decreasing the oil and water viscosity, but the effect of oil viscosity was less.In order to investigate the sensitivity of gravity on imbibition rate, the vertical cube core was modeled by proposed numerical method. The capillary and gravity forces were driving forces of water imbibition, but each of these forces could act as dominant force to control the imbibition rate. According to the matrix property and the position of the matrix and the fracture, the dominant force was determined.Increasing the height of core increased the effect of gravity and decreased the effect of capillary forces. Neglecting the gravity force caused a lot of error in predicting the oil recovery from high reservoirs by imbibition process.This project also presented a numerical modeling of imbibition phenomenon into an oil saturated cylindrical core for studying effect of boundary condition and shape factor on spontaneous imbibition. By using the proposed model, the most effective boundary condition for achieving the maximum oil recovery could be determined. The oil recovery was increased with increasing the permeable surfaces in contact with water. Keywords: mathematical modeling of fractured reservoirs, spontaneous imbibition, counter-current imbibition, capillary diffusivity coefficient, spontaneous imbibition up scaling