Abstarct: Explosion problems can be examined in different environments. Due to the lesser-known nature of soil types and extent of the equations of state explosion problems need careful analysis. Because of difficulties in laboratory explosion test, numerical models is used to analyze this phenomenon. Using the smooth particle hydrodynamics,SPH methodology avoids disadvantages of traditional numerical methods in treating large deformations in the extremely transient explosion process. Since explosion crater in soil is an important problem and most of the studies are experimental, this thesis it is tried to investigate the craters diameter and height caused by the different amounts of explosives. The model is programmed with Fortran language and SPH methodology. The craters, pressure caused by explosion in soil and soil surface changes are studied for two types of soil with different properties. Each type of soil, studied for different explosive loading with different dimensions. To validate the model, the results of a laboratory study were used and it is shown that they are consistent with the numerical results of this study. Finally craters in a two laxyer soil, soil slope and explosion on the saturated soil and underwater is studied. This code can be used for modeling of soil explosion and craters. According to the obtained results, it is concluded that the maximum explosion pressure in dense soil is more than loose soil. Also the arrival time to the maximum pressure reduced for condense soil because the sound speed and density in dense soil is more than loose soil. In both type of soil, increasing the explosive load, resulted more pressure and bigger crater is constructed. Craters dimension in condense soil is less than loose soil. For two laxyer soil, if the looser soil supposed as the upper laxyer, the crater dimension decreased in height and constant in width.Also the craters in soil slopes. The explosion on the saturate soil which is under water shows that the explosion bubble in the water is greater than saturated soil.