Foam concrete is a significant engineering research topic considering its lightweight, high homogeneity, low cost, and low thermal conductivity (<0.5 W/mK). These reasons enhanced good property become an important achievement and modify the use of foamed concrete. This paper includes a review of the effect of added material to the foamed concrete (coarse fly ash, fine fly ash, and fiber reinforcement) on the elastic modulus of concrete. The results show that the addition of fly ash as a fine aggregate decreases the elastic modulus value (E-value) by 20% compared to specimens without fly ash, while reducing dry shrinkage by 35% when 30% of cement is replaced with fine fly ash of density equal to 1400 Kg/m3, also reducing the heat of hydration by adding 0.15 % polypropylene fiber, increasing the E-value by 14.41 % for a density of 1600 Kg/m3 and increasing the E-value by 65.6% for a density of 1800 Kg/m3. The E-value of foamed concrete is equal to about 0.25 of the E-value of normal weight concrete, and the value of static modulus of elasticity typically varies between 1000 and 8000 MPa in foamed concrete. Also, proposed models given in the literature to predict modulus of elasticity in different situations with different additional materials are given in this paper.