It could be any number of things, but it reminds me of Gold Medal -- I'll put a link to the HelpMeFind photos. Click on thumbnails for a bigger picture and on Rose tab for a description:
You know, Patricia, I think you're right -- it's not Gold Medal after all. But I just know I've seen the variety in heyzues' photo before; both the blooms and the foliage look familiar to me.
I'll keep thinking and try to figure out what it could be, or maybe someone else wants to guess.
This looks very similar to the rose I've been trying to identify for months. Mine was planted by my parents, both of whom are dead now, probably planted sometime in the 50's.
