Now it is generally accepted that one of the important generalizations of the concept of computability is \(\Sigma\)-definability (generalized computability) in admissible sets. This generalization has made possible to study computability problems over arbitrary structures, for instance, over the field of real numbers. A crucial result of classical computability theory is the existence of an universal partially computable function. It is known that an universal \(\Sigma\)-predicate exists in every admissible set, but this is false for \(\Sigma\)-functions. Therefore, it is interesting to know which conditions on \(\mathfrakM\) guarantee the existence of an universal \(\Sigma\)-function in the hereditarily finite admissible set \(\mathbb(\mathfrakM)\) over \(\mathfrakM\). In this talk we discuss the problem of the existence of an universal \(\Sigma\)-function in the hereditarily finite admissible set over some locally finite structures.