Etiquette in applying for undergrad research I am currently looking into applying for funding as an undergraduate summer research assistant.  At the moment, two professors have agreed to allow me to work with them.  Since I can't be sure that the funding application would be accepted, I am considering accepting the offer from both professors and going forward with applying for funding with both professors - is this a good idea?  If so, should I let both professors know this?  If not, could I try asking the prof's permission to do this, or would it be in my best interest to just decide on my top choice now and just pursue that?

Thanks in advance!
You could do it with the permission of both professors, I think, though the funding agencies might disagree with that. But don't do it without at least their agreement. If the professors are at the same institution, perhaps you could work out something that they both participate in. There might be issues with that, of course. 

But asking them both might also give you better information about which would be easier to work with. If one seems cooperative and the other not, it might be an indicator. 

In general, asking is always a good thing to do.