The influence of viscoplastic rheological features on the Rayleigh-Bénard convection is investigated by numerical means in order to compare with first experimental results given by Darbouli et al. The fluid is modeled by a regularized Herschel-Bulkley law which is often used to fit numerous pasty fluids. Natural convection in a two-dimensional square cavity heated from below is considered. Critical values of Oldroyd number Od and yield number Y are provided. Numerical results highlight a stabilizing effect of the yield stress as well as a destabilizing effect of increasing shear-thinning coefficient n as the increase in n enhances the heat transfer in the range of our calculations. Unyielded regions are located in the square corners of the cavity and in the cavity where convection occurs. The unyielded zones size increases with the increase in Od and can invade all the cavity for sufficiently large values of Od.