The study investigates inequalities in access to social capital based on social class origin and immigration background and examines the role of transnational ties in explaining these differences. Social capital is measured with a position generator methodology that separates between national and transnational contacts in a sample of young adults in Sweden with three parental backgrounds: at least one parent born in Iran or Yugoslavia, or two Sweden‐born parents. The results show that having socioeconomically advantaged parents is associated with higher levels of social capital. Children of immigrants are found to have a greater access to social capital compared to individuals with native background, and the study shows that this is related to transnational contacts, parents’ education and social class in their country of origin. Children of immigrants tend to have more contacts abroad, while there is little difference in the amount of contacts living in Sweden across the three groups. It is concluded that knowledge about immigration group resources help us predict its member's social capital, but that the analysis also needs to consider how social class trajectories and migration jointly structure national and transnational contacts.