A flat tax rate on income has gained popularity in European countries. This paper assesses the attractiveness of such a flat tax in achieving redistributive objectives with the least cost to labour market performance. We do so by using a detailed applied general equilibrium model for the Netherlands. The model is empirically grounded in the data and encompasses decisions on hours worked, labour force participation, skill formation, wage bargaining between unions and firms, matching frictions, and a wide variety of institutional details. The simulations suggest that the replacement of the current tax system in the Netherlands by a flat rate will harm labour market performance if aggregate income inequality is contained. This finding bolsters the notion that a linear tax is less efficient than a non-linear tax to obtain redistributive goals.