Cell reorientation and migration play crucial roles in various physiological and pathological processes, including organ development, tissue repair, tumor progression and invasion. Consequently, they remain central topics of scientific investigation. Experimental studies have demonstrated that cell dynamics are influenced by a range of external cues, particularly chemical and mechanical signals. While chemotaxis has been extensively studied, mechanisms underlying migration in response to mechanical stimuli - such as stress/strain (tensotaxis) - remain less understood. In this context, we propose two mathematical models to investigate single-cell migration induced by mechanical cues, focusing respectively on fibroblasts and neurons. In both cases, the cell is modeled as a point particle characterized by its position, polarization direction and motility (speed). The latter two can be driven by distinct stimuli. Stochastic components are also included to account for the random Brownian-like motion typical of cell behavior. In the first model, the evolution of the cell's polarization direction and motility is given by non-local integro-differential equations that capture the cell's capacity to sense mechanical properties of the substrate in its surrounding environment. The second model, which addresses early development of neurons, describes the dynamics in terms of position, polarization direction and motility of the growth cone. The governing equations describe both the reorientation and growth of neurons in response to cyclic stretching of the underlying substrate, and tubulin production in the soma, respectively. To validate the models, we present numerical simulations that qualitatively replicate experimental conditions.