Can I use the Gelish polish with the Shellac base and top coat?

I was wondering the same thing. I love shellac but like the gelish colors. I can't use the gelish base and top coast because I'm allergic to it and end up with very damaged and painful fingers

Simple answer - no.
They are both two week manicures, and they are both cured under UV light. But that is where the similarities end. Gelish is a Gel Polish, Shellac is a unique product unlike anything else on the market.
You cannot mix systems, clients are paying for either Gelish or Shellac and therefore you should provide the complete system. If you don't you run the risk of service breakdown, allergic reaction, breach of trade descriptions, insurance not covering the treatment.

It shouldn't be a problem as they are quite similar systems. Although as they are not designed to work together you might find that it may not last as long as they would if you were to use the systems exclusively. However if it is the financial aspect that is putting you off you can find a more budget savvy product to use with in harmony gelish, which is a product ( easily found on eBay) called bluesky gelish where the top and the base coat together can be bought from around £15, I use this on myself at home and I found it can last just as long as the shellac and inharmony gelish systems, however I think it may be inappropriate to use this in a salon as it is more of a personal brand than a commercial brand. I hope this helps.

They do work together, but you may find that the manicure will not last as long as it does if you only use one system at a time as you should. Shellac base coat only needs to be cured for 10 seconds in a UV lamp and does not require dry brushing, wheras the Gelish needs to be cured for 1 minute and you also should dry brush the foundation coat and use PH bonder. As you are only using it on yourself I cant see a problem.

Shellac is a hybrid gel polish, Gelish is a gel polish, similar but different. I prefer Gelish over Shellac. I am building up a collection of colours, use Icon, Gelish and Daisy. I have mixed brands in one application, and they turn out beautifully. Gelish do avertise that there system will work with another. Love Daisy Base Coat and Gelish Top Coat. Gelish Base Coat has to be rubbed with a dry brush before colour application and I don't like the idea, its possible the product may get on to the soft tissue. Daisy like Gelish claim their product can be mixed with others.

They would probably work together as they are both based around the same system ... Hybrid gel polishes! Althought I'm not sure the suppliers would be best pleased...lol
You have nothing to loose if experiementing on your own nails but I wouldn't use this method on a client it's just not professional. Personally I only use Shellac, the original hybrid nail polish x

No you shouldn't mix different systems.

They won't work you will end up with a service break down! Also if it's for use at home on yourself are you qualified to do so?

No they won't work together. Shellac is not a gel polish

Because these are brands and you are using a product, they should work fine together.
But just in case I would suggest giving the brands an e-mail to make sure that it will be okay.