Compressive strength is one of the most important mechanical properties of concrete. Both of shape and size of specimens affect on the value of compressive strength which varies according to the country where test occurred and standard specimens used. A numerical investigation in this work by using one of the powerful and famous finite element analysis program, ANSYS, was done to predict a real size factor In the present work, a numerical program using ANSYS to study the effect of specimen size on the stress and strain behavior of concrete specimens was conducted. Cubic concrete specimens of six sizes 70,100,150, 200, 250 and 300 mm and cylindrical specimens of four sizes 70,100,150 and 200 mm in diameter with aspect ratios one and two were idealized under monotonic loading condition. Three different strength levels including 30, 50 and 70 MPa were investigated in this work. Studying the behavior of stresses and strains under strain condition for each level of concrete strength was conducted. For the investigated shapes and sizes there is a decrease in the value of ultimate stresses and strains with increase in specimen size. The effect of specimen size is very small in cylindrical specimens with aspect ratio equals two and does not clear in cylindrical specimens with aspect ratio equals one. The numerical data were analyzed and correlated for cubic specimens to obtain a mathematical formula through which could be predicted the size effect factor for any cubic specimen size. Acceptable agreement between the predicted data and previously published experimental results was found.