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Its hard to tell for sure, but it looks to me like it doesn't have one. I've looked at other sites and nobody mentions a dust cover. So I'd assume its not there. You can contact Buds to be certain at 1-859-368-0371

It looks like its not there, but a tiny chance it may be in the down position? But really looks more like its not there. Incredible they wouldn't put one on it.

I don't think it has one. Researching msr 10's I haven't seen any with a dust cover. You could call savage to be 100 percent sure but I'm 99 percent sure it doesn't.