Recent empirical research has shown that income per capita in the aftermath of natural disasters is not necessarily lower than before the event. In many cases, income is not significantly affected and surprisingly, can even respond positively to natural disasters. Here, we propose a simple theory based on the neoclassical growth model that explains these observations. Specifically, we show that GDP is driven above its pre-shock level when natural disasters destroy predominantly residential housing (or other durable goods). Disasters destroying mainly productive capital, in contrast, are predicted to reduce GDP. Insignificant responses of GDP can be expected when disasters destroy about equally residential structures and productive capital. We also show that disasters, irrespective of whether their impact on GDP is positive, negative, or insignificant, entail considerable losses of aggregate welfare.