A simple and realistic model of an excitable chemical system in which running impulses can be observed is studied. Mesoscopic characteristics of the model are obtained by numerical simulations of the master equation for spatially extended system. Velocity of the impulse and its shape obtained in the simulations agree well with the phenonenological description. For small diffusion coefficients, fluctuations grow locally and create impulses of excitations. Formation of such impulses cannot be described by the phenomenological approach. However, if an excitation is sufficiently developed, its subsequent evolution can be predicted with reasonable accuracy by phenomenological equations.