Occupational specificity of human capital motivates an important role of occupational reallocation for the economy's response to shocks and for the dynamics of inequality. We introduce occupational mobility, through a random choice model with dynamic value function optimization, into a multi-sector/multi-occupation Bewley (1980)-Aiyagari (1994) model with heterogeneous income risk, liquid and illiquid assets, price adjustment costs, and in which households differ by their occupation-specific skills. Labor income is a combination of endogenous occupational wages and idiosyncratic shock. Occupational reallocation and its impact on the economy depend on the transferability of workers' skills across occupations and occupational specialization of the production function. The model matches well the statistics on income and wealth inequality, and the patterns of occupational mobility. It provides a laboratory for studying the short- and long-run effects of occupational shocks, automation and task encroaching on income and wealth inequality. We apply the model to the pandemic recession by adding an SIR block with occupation-specific infection risk and a ZLB policy and study the impact of occupational and aggregate labor supply shocks. We find that occupational mobility may tame the effect of the shocks but amplifies earnings inequality, as compared to a model without mobility.