As Tracy B notes above, yes, a person can be imprisoned for falling behind on child support payments, but imprisonment is not often the outcome. The court tries to remedy an issue before punishing it in family matters so as to minimise the additional burden on other branches of the justice system. If you're experiencing problems with child support, contact the Child Support Agency and apply to have the other party's child support payments garnished directly from their wages, rather than paid through a private agreement.