This paper investigates empirically how similarity of demand structures - approximated by similarity of income distributions - affects trade patterns along both the extensive and intensive margin. The idea that similarity of demand structures intensifies trade goes back to the well-known Linder hypothesis. Based on a sample of 102 countries, I find that bilateral trade volumes are increasing in the overlap of two countries income distributions. This effect is driven by both the extensive and intensive margin. I establish two novel measures of income similarity - the average income level of the overlap area and the range of incomes for which two distributions overlap - and document that both are important determinants of bilateral trade margins. My analysis shows that the positive relationship between similarity of income distributions and bilateral trade margins is present at the aggregate and disaggregate level of trade flows.