A computer model (SprinklerMod) was developed to simulate hydraulics of sprinkler irrigation systems. The objective of this paper is to describe mathematical background of this model for simulating pressures and discharges of sprinklers along the laterals. The model is capable of designing two types of laterals: laterals with fixed sprinklers and laterals with portable sprinklers. The model shows the simulation results in the forms of tables and graphs. Laterals with one or two diameters on uniform or non-uniform slopes can be designed. The model provides graphical presentation of percentage of sprinkler pressure variations for different lateral inside diameters. The Hazen- Williams equation was used for the calculation of friction losses. The required input parameters for lateral simulation are lateral type, desired sprinkler operating discharge and pressure head, spacing between sprinklers, distance of first sprinkler from lateral inlet, number of sprinklers operating on the lateral, riser height, Hazen- Williams pipe friction coefficient and lateral longitudinal slope or field elevations at each of the sprinklers on the lateral. Laterals are simulated such that average sprinkler pressures and discharges become equal to the values requested by the designer. Iterative procedures were implemented to simulate sprinkler pressures and discharges on laterals and the Newton- Raphson iterative method was used for calculating pressure of each of the sprinklers on the laterals with portable sprinklers. In order to evaluate the model, some example results of the model were compared with classical design results. Since there is no formula for the calculation of the required lateral inlet pressure in classical design of laterals with portable sprinklers in the scientific references, a new formula was developed. Averages of absolute percentage of variations of lateral inlet pressures for laterals with fixed sprinklers and with one or two-size diameters ranged from 0.3 to 0.7 percent, respectively. This value for laterals with portable sprinklers was 0.1 percent.