Ultrashort-pulse lasers are an established technology for micromachining and have a great future. A major challenge remains the search for suitable laser parameters and a scanning strategy. To date, this has been achieved mainly by conducting experiments and measuring the resulting surfaces. The use of modeling methods for this purpose is not yet practical for industrial processing. In this work, the recently introduced geometric modeling method for pulsed laser ablation is applied to ultrashort laser ablation and extended to consider the power dependence of the process footprint and the pointing stability during ablation. This work highlights this modeling method to cover a wide range of process parameters in a time-saving manner and to simulate laser micromachining in real time. Furthermore, the influence of the processing height compared to the focal height on oxygen-free copper and steel 1.4034 was investigated. For both the ablation depth is decreased while simultaneously increasing the ablation width. For oxygen-free copper, the ablated volume is insensitive to changes in the processing height, which is not the case for steel 1.4034. The results also show the influence of the pulse repetition rate on the change in the shape of material removal and its influence on process stability.