The idea that goods or factors of production may not be perfectly divisible has important implications for many areas of economics. This paper introduces both types of indivisibilities into the standard Ricardian model of international trade. Indivisibilities give rise to new results compared to the standard model with perfectly divisible goods and factors of production. Both types of indivisibility may result in complete specialisation even in autarky, while goods indivisibility may result in (ex ante) identical consumers consuming different bundles of goods, and hence enjoying different levels of welfare. Both types of indivisibilities lead to efficiency losses relative to the perfectly divisible case. International trade may eliminate efficiency losses resulting from indivisibility in the factors of production, but not those resulting from goods indivisibility. This suggests that the presence of indivisibilities leads to a second-best world, with the consequent implications for policy. The results of the paper are consistent with existing empirical evidence.