I've heard it can be done. Cocketiels, as a rule, are friendly and socialable and will generally leave other species alone. Though I'd suggest having a LARGE cage.

I am not an expert but i dont think it should be done. Cockatiels have a much stronger beak. and they often like to peck at other birds feet. i think that they should be kept seperate, dont take this as a gospel or any thing. but you should ask your local pet place or parrot place were you purchased them.

Finches are generally very gregarious birds and need company, preferably from one or more of their own variety. A finch alone by itself is usually an unhappy bird. Some varieties mix well with other finches. Some varieties will get along well with other finches most of the time, but don't after they pair off for breeding. And some varieties are quite aggressive and cannot be kept with other finches at all. A cage or an aviary is an unnatural habitat for them and they cannot get away from other animals the way they can in the wild. As for getting along with non-finches, it depends on a couple of factors. If the finch is one of the more aggressive varieties, chances are it won't. Finches are usually afraid of larger birds. Remember, they are very small and pretty near the bottom of the food chain. They tend to view other animals as creatures who want to eat them. A finch will only rarely be friendly to a human; they are not affectionate the way some birds can be. Think of finches as eye- and ear-candy and don't be offended if they always 'have a bird' when you get close. If you put them in a cage with a larger bird, there is a good chance they will feel threatened. If they cannot get far enough away from the larger animal, they will become stressed. They can get along with smaller birds, such as canaries, but I would be very hesitant about combining them with anything larger. They won't ineract with the other bird, so don't expect them to provide companionship for another species or to receive it in return.

I had kept finches (zebras, gouldians, javas) in an aviary with cockatiels for 8 years and never had a whisper of a problem. The aviary has to be large enough that the finches don't have to be too close to the cockatiels if they don't want, and put the finch feeding stations and accessories on the opposite end of the aviary. Also try putting plants in there (makes them feel safer) and make sure there are plenty of perches on different levels so they don't have to share the same perch. Although I and many other people have never had problems, some people have. It may depend on the conditions and individual personality of the bird, but small hookbills have been known to pester and even kill finches. So always keep a close eye on what is going on. Birds of different species usually just tolerate each other and leave each other alone. Although someone I know had a finch that showed affection towards one of the cockatiels, and I had a chinese painted quail and a ringneck dove that would always sit next to each other and preen each other.