This paper addresses two hot topics of the contemporary debate, social capital and economic growth. Our theoretical analysis sheds light on decisive but so far neglected issues: how does social capital accumulate over time? Which is the relationship between social capital, technical progress and economic growth in the long run? The analysis shows that the economy may be attracted by alternative steady states, depending on the initial social capital endowments and cultural exogenous parameters representing the relevance of social interaction and trust in well-being and production. When material consumption and relational goods are substitutable, the choice to devote more and more time to private activities may lead the economy to a social poverty trap, where the cooling of human relations causes a progressive destruction of the entire stock of social capital. In this case, the relationship of social capital with technical progress is described by an inverted U-shaped curve. However, the possibility exists for the economy to follow a virtuous trajectory where the stock of social capital endogenously and unboundedly grows. Such result may follow from a range of particular conditions, under which the economy behaves as if there was no substitutability between relational activities and material consumption.