A variety is solid if each of its identities holds as a hyperidentity, i.e., if it is satisfied also whenever the fundamental operations are replaced by terms of the same arity. Although an infinite number of solid varieties of semigroups is known, only very few examples of solid varieties are known for other similarity types. The paper contains three constructions which produce infinite chains of solid varieties. The first one is a generalization of the normalization of a variety which was already developed by the last author. It produces an infinite chain of solid varieties of type (\(n\)). The second construction generalizes the rectangular nilpotent varieties of type (2) to type (\(n\)). The third one uses the consequences of idempotency to construct an infinite chain of solid varieties of any type.