The toughness \(t(G)\) of a noncomplete graph \(G\) is defined as \[t(G) = \min\left\{\frac{|S|}{w(G – S)} \mid S \subset V(G), w(G – S) \geq 2\right\}\] and the toughness of a complete graph is \(\infty\), where \(w(G – S)\) is the number of connected components of \(G – S\). In this paper, we give the sharp upper and lower bounds for the Kronecker product of a complete graph and a tree. Moreover, we determine the toughness of the Kronecker product of a complete graph and a star, a path, respectively.