We present a description of our numerical code BLAZAR. This code calculates spectra and light curves of blazars during outbursts. The code is based on a model in which the non-thermal flares in blazars are produced in thin shells propagating down a conical jet with relativistic velocities. Such shells may represent layers of a shocked plasma, enclosed between the forward and reverse fronts of an internal shock. In the model adopted by us, the production of non-thermal radiation is assumed to be dominated by electrons and positrons which are accelerated directly, rather then injected by pair cascades. The code includes synchrotron emission and inverse-Compton process as the radiation mechanisms. Both synchrotron photons and external photons are included as the seed photons for Comptonization. At the present stage, the code is limited to treat the inverse Compton process only within the Thomson limit and is specialized to model radiation production in the flat spectrum radio quasars. As an example, we present the results of modeling an outburst in 3C 279 – the most extensively monitored γ-ray – bright quasar.