The isolated toughness i𝜏(G) of a noncomplete graph G is defined as:This isolated toughness parameter is closely related to the existence of factors and fractional factors in graphs. These factors and fractional factors are well-studied within graph theory, and have various applications in several fields related to computer science. In this article, we pay our attention to the computational complexity of computing the isolated toughness. We present polynomial algorithms for computing the exact value of i𝜏(G) for interval graphs and for split graphs, two well-studied special graph classes.