The determination of the morphology of galaxy clusters has important repercussion on their cosmological and astrophysical studies. In this paper we address the morphological characterisation of synthetic maps of the Sunyaev--Zeldovich (SZ) effect produced for a sample of 258 massive clusters ($M_{vir}>5times10^{14}h^{-1}$M$_odot$ at $z=0$), extracted from the MUSIC hydrodynamical simulations. Specifically, we apply five known morphological parameters, already used in X-ray, two newly introduced ones, and we combine them together in a single parameter. We analyse two sets of simulations obtained with different prescriptions of the gas physics (non radiative and with cooling, star formation and stellar feedback) at four redshifts between 0.43 and 0.82. For each parameter we test its stability and efficiency to discriminate the true cluster dynamical state, measured by theoretical indicators. The combined parameter discriminates more efficiently relaxed and disturbed clusters. This parameter had a mild correlation with the hydrostatic mass ($sim 0.3$) and a strong correlation ($sim 0.8$) with the offset between the SZ centroid and the cluster centre of mass. The latter quantity results as the most accessible and efficient indicator of the dynamical state for SZ studies.
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