A pinched pressure-driven flow injection on a microchip is numerically simulated in order to optimize the relative values of the operational parameters. The geometry studied is a two-dimensional rectangular channel featuring a cross-junction with a large depth-over-width ratio. The hydrodynamic and convection-diffusion equations are solved for the two steps of the process: first, the sample solution is pinched into the transversal channel (injection channel), and then it is injected into the longitudinal one (separation channel), where the time evolution of the concentration is analyzed for different types of the detectors. Electroosmotic flow calculations have also been performed and have shown a good agreement with literature. The results for pressure-driven flow point out that the shape of the detection signal is strongly dependent on the velocity in the separation channel and on the position of the detection probes. The so-called double-humped peak, caused by the parabolic flow profile at high driving flow rate is analyzed. A tight pinch greatly decreases the amount of injected sample and, consequently, the signal sensitivity without increasing its quality. A proper pullback of the sample during the separation process can decrease the tailing due to the sample leakage from the injection channel. Although a high sample pullback causes a considerable decrease in the signal sensitivity, it also greatly enhances the peak resolution. Finally, it is shown that a wider injection channel with high sample pullback ensures an improved signal sensitivity with good resolution.