Three sets of data for shock pair disturbances, which are assumed to have been formed from stream-stream interactions, are modeled by using two time-dependent numerical codes. One code solves the fluid dynamic equations, and the other solves the magnetohydrodynamic equations. The observed disturbances are simulated by superimposing an initial interaction (a pulse in the dependent variables) onto the ambient solar wind and then following the time evolution of the resulting disturbance with the numerical codes. The magnitude of the initial interaction is such that the calculated solar wind agrees with the solar wind observed by the space probe both prior to the arrival of the forward shock at the space probe location and following passage of the reverse shock. The location of the initial interaction is iteratively chosen so that the simulated time interval between the forward and reverse shocks at the space probe location agrees with the measured value. The large-scale structure in the disturbance is reproduced if (1) the magnetic field and azimuthal velocity are included (that is, if the code which solves the magnetohydrodynamic equations is used), (2) the time dependence of the initial interaction is appropriately selected, and (3) the observed nonradial shock normals are accounted for in the modeling procedure. The relative importance of each of the above requirements varies for each set of data. The first and third requirements played the dominant roles in one data set, while for the other two data sets the second requirement was probably the most important. Hence it is recommended that all three requirements be met in attempting to simulate data for shock pair disturbances.