  Let $G_1\sq G_2$ denote the graph obtained from $G_1+G_2$ by adding new edges
from each vertex of $G_1$ to every vertex of $G_2$. In this paper, the critical
groups of the graphs $K_m\sq P_n$$(n\geq4)$ and $P_m\sq P_n$$(m\geq4,n\geq5)$
are determined.
