The use of ultrafast lasers (pulsed lasers with pulse lengths of a few picoseconds or less) offers the possibility for minimally invasive removal of soft ophthalmic tissue. The potential for using pico- and femtosecond pulses for modification of scleral tissue has been reported elsewhere [1-6] and has resulted in the introduction of new, minimally invasive, procedures into clinical practice [3, 5-10]. Our research is focused on finding optimal parameters for picosecond laser machining of scleral tissue without introducing any unwanted collateral damage to the tissue. Experiments were carried out on hydrated porcine sclera in vitro, which has similar collagen organization, histology and water content (∼70%) to human tissue. In this paper we present a 2D finite element ablation model which employs a one-step heating process. It is assumed that the incident laser radiation that is not reflected is absorbed in the tissue according to the Beer-Lambert law and transformed into heat energy. The experimental setup uses an industrial picosecond laser (TRUMPF TruMicro 5x50) with 5.9 ps pulses at 1030 nm, with pulse energies up to 125 μJ and a focused spot diameter of 35 μm. The use of a scan head allows flexibility in designing various scanning patterns. We show that picosecond pulses are capable of modifying scleral tissue without introducing collateral damage. This offers a possible route for minimally invasive sclerostomy. Many scanning patterns including single line ablation, square and circular cavity removal were tested.