A probabilistic model was developed that applies to the analysis of erratic movements made by animals foraging in a stochastic environment. This model is a first order correlated random walk model in which the following two biological constraints are integrated into the Brownian motion model: bilateral symmetry and the cephalocaudal polarization that leads to a tendency to go forward. The main properties of the model were studied by numerical simulations using a pseudo-random generator. It was found that the spatial pattern of search paths could be quantified by a single numerical index of sinuosity. Some advice on the concrete use of this model is given. Correlated random walk diffusion was studied in relation to the sinuosity by analysing the probabilistic distribution of the bee-line distance between the first and last points of a path. Some theoretical applications of this model are developed.