This article advances the existing theoretical analysis of pulsed electric field (PEF) treatment, an application of pulsed power technology. PEF treatment has attracted significant attention due to its potential to be used for non-thermal biological sterilization and inactivation of microorganisms, bio-extraction, and for the possible role that it may play in the treatment of tumors and cancers such as in electrochemotherapy. However, the bioelectric effects of impulsive electric fields on different biological matter are not yet completely understood. Further advances in this direction would aid in the optimization of the necessary pulse waveforms to achieve the desired PEF effects in, for example, various biomedical and food processing industries. In this work, the commonly used multi-shell model of microorganisms utilized for the analysis of cell transmembrane potentials (TMPs) has been generalized to include an arbitrary number of layers. Analysis has been conducted on the novel mathematical model, which demonstrated the ability to estimate TMPs and relaxation times for an n-shell topology using a meshfree approach. This allows for complex many-shelled cell models to be analyzed, free from the limitations of spatial or temporal discretization, i.e., those present when using finite-element or finite-volume based methods. Using this model, the effects that the pulse rise-time and pulse duration have on the developed TMPs in a single 6-layer Saccharomyces cerevisiae yeast, and under the microsecond-PEF regime, have been investigated. It has been found that the pulse rise-time has a far lesser effect on the PEF action compared to the modulation of the pulse duration, supporting past experimental observations. The role of the electrical conductivity of the extracellular medium (and considering induced changes in the cell components) has additionally been studied, under low (σ = 1 mS/m), medium (σ = 50 mS/m), and high (σ = 100 mS/m) conductivity values. Estimations provided by this model may support the optimization of pulse waveforms for current and future PEF applications, and for the analysis of complex multilayered cell structures under pulsed electrical stress.