Supernova remnants (SNRs) are widely considered to be sites of Galactic cosmic ray (CR) acceleration. Vela is one of the nearest Galactic composite SNRs to Earth accompanied by the Vela pulsar and its pulsar wind nebula (PWN) Vela X. The Vela SNR is one of the most studied remnants and it benefits from precise estimates of various physical parameters such as distance and age. Therefore, it is a perfect object for a detailed study of physical processes in SNRs. The Vela SNR expands into the highly inhomogeneous cloudy interstellar medium (ISM) and its dynamics is determined by the heating and evaporation of ISM clouds. It features an asymmetrical X-ray morphology which is explained by the expansion into two media with different densities. This could occur if the progenitor of the Vela SNR exploded close to the edge of the stellar wind bubble of the nearby Wolf-Rayet star $gamma^2$Velorum and hence one part of the remnant expands into the bubble. The interaction of the ejecta and the main shock of the remnant with ISM clouds causes formation of secondary shocks at which additional particle acceleration takes place. This may lead to the close to uniform distribution of relativistic particles inside the remnant. We calculate the synchrotron radio emission within the framework of the new hydrodynamical model which assumes the supernova explosion at the edge of the stellar wind bubble. The simulated radio emission agrees well with both the total radio flux from the remnant and the complicated radio morphology of the source.