  The Josephson effect is theoretically studied in two types of SQUIDs
consisting of $s$ wave superconductor and Sr$_2$RuO$_4$. Results show various
response of the critical Josephson current to applied magnetic fields depending
on the type of SQUID and on the pairing symmetries. In the case of a $p_x+ip_y$
wave symmetry, the critical current in a corner SQUID becomes an asymmetric
function of magnetic fields near the critical temperatures. Our results well
explain a recent experimental finding [Nelson et. al, Science \textbf{306},
1151 (2004)]. We also discuss effects of chiral domains on the critical
current.
