The symmetric cardinality constraint is described in terms of a set of variables X={x1,...,xk}, which take their values as subsets of values V={v1,...,vn}. It constraints the cardinality of the set assigned to each variable to be in an interval [lxi,cxi] and at the same time it restricts the number of occurrences of each value vj in V in the sets assigned to variables in X to be in an other interval [lvj,cvj]. In this paper we introduce the symmetric cardinality constraint and define set constraint satisfaction problem as a framework for dealing with this type of constraints. Moreover, we present effective filtering methods for the symmetric cardinality constraint.