While case...esac is fine, if you have your heart set on using 'expr' you can use expr this way:

expr $parameter : ".*$search" >/dev/null && echo Found!!!

In this form, expr returns the # of characters matched from the beginning of $parameter. That's why I had to put a ".*" in the beginning of the search string. Also, expr writes the number of characters matched to stdout (so I directed to /dev/null). Of course, you can just use this value in a test like this:

if [ expr $parameter : ".*$search" -gt 0 ]
then