Neuronal stimulation with electrodes is an actively researched technology that has many therapeutic and diagnostic applications. A promising subfield is stimulation of the cerebral cortex via microelectrodes, which is used or researched as treatment for a variety of conditions such as pain and blindness. One challenge facing these practical applications is a lack of knowledge regarding the exact effects of stimulation on neurons in the tissue. This may lead to unwanted effects including failure of medical interventions and prostheses. One of the topics that are still under dispute is the upper stimulation threshold, its causes and the conditions under which it manifests. The upper stimulation threshold is an effect in which a neuron ceases to be excited by stimulation if a certain current strength is exceeded but which is still far below an intensity that would damage the cell. Several causes have been proposed for this. One is current reversal, in which sodium ions pass the membrane in the direction opposite to what is needed for excitation. Another is anodal surround block, where parts of the cell experience a drop in membrane potential upon stimulation instead of a rise that would lead to excitation. The aim of this work was to investigate whether an upper threshold could be found and its causes identified for different stimulation regimes in the model of a single layer 5 neocortical pyramidal cell. For comparison, several simpler models were also used, with one consisting just of a spherical soma, one with an axon attached to the soma, one with an additional single dendrite and finally a two-dimensional version of the pyramidal cell. The pyramidal neuron was chosen because it is one of the cell types targeted with cortical implants and because its dimensions and membrane properties are relatively well known. The geometry of the pyramidal cell in the model was taken from the tracing of a real cell and the original soma replaced with a special spherical version to make it suitable for close quarter stimulation. The implementation was done with the software NEURON and is based on a multi-compartment model using Hodgkin-Huxley channel kinetics. Active channels and mechanisms known to exist in real layer 5 pyramidal cells were integrated into the model. Cathodic extracellular stimulation using a point sized current source was applied with varying intensity, duration and electrode position. Cellular voltages and sodium currents were recorded for the different models and thresholds identified. The results confirmed the existence of an upper threshold for all models and stimulation modalities. For the model consisting only of a soma, net sodium current reversal cold be ruled out as a cause for the upper threshold at least for short stimulation durations. It was not possible to draw any other conclusion about the causes of the upper thresholds with much certainty for any model. In some cases, even strong current reversal during stimulation was not enough to prevent excitation. Some patterns across different models could be identified. Stimulation near the dendrites was more difficult than in other regions and in the case of the three-dimensional pyramidal cell sometimes completely failed. The soma was easier to stimulate and had higher upper thresholds if other neurites were attached to it. Stimulation near the axon generally led to a large stimulation window with high upper thresholds. These results of this thesis should shed some light on the reaction of pyramidal cells to different stimulation modalities and the question under what circumstances a failure of excitation can be expected.