DoubleD

I'm a "mech" engineering student. I'd like to pursue a PhD in "aerospace" engineering.
My school doesn't have an aerospace program. The research I'm currently doing isn't really aerospace related. There is really nothing that related going on at other labs either.

My goal is get into a top institution.

Since my undergrad research isn't really that related, do you guys think this will be a weak point when I apply?

tetrahedr0n

Not really, especially if it's something outside of your control. In your research statement (in the application) you can try to tie your research to the research you plan to do in grad school. Even in the worst case, showing that you're capable of performing research in an engineering field is a valuable thing.

TaciturnType

The professors at your school might not be researching aerospace directly, but I'm willing to bet at least some of them are researching something in mechanical engineering that's related to aerospace.

There are countless components that go into aerospace design, and they hire nearly every engineering major. Anything such as fluid/heat flow, dynamics, mechanics/stress of materials, and others are important topics in aerospace design. If you explain how your research in one of these areas can be applied to improving aerospace systems, that makes it relevant. You might still have some disadvantages, but the engineering fields are becoming so interdisciplinary nowadays that there's a place for everybody.