My wife is Ukraine , i am British.
During WWII , her grandmother and grandfather (both Ukrainians) were taken by force by the Germans to Vienna , Austria. Their baby was born in Vienna. After the war finished grandmother and mother were sent back to Ukraine.
We have all documents showing this , dates , movement etc.
Can my wife claim Austian citizenship by descent ?

You would have to check on Austrian law. Not all countries consider those born of foreign parents to be automatically citizens.

Surely they're Ukrainian by descent, rather than Austrian?

Many countries including German-speaking ones didn't until recently allow citizenship by birth, so a baby born to Ukrainians in Austria might still just be Ukrainian.

You could contact the Austrian embassy and ask about this.

You really need to contact the Austrian authorities on this one, but this website has some of the rules for you:
http://www.wien.gv.at/english/admini...ip/obtain.html

It seems being born in Austria is not enough to get citizenship.

You should seek out professional advice.

This is *extremely* complex, involving (1) many major historical events and (2) the laws of both Austria and Ukraine (and per the examples below, possibly the laws of Germany or Israel). And the boundaries of Ukraine and other countries radically changed over time. (My wife’s mother was from a small German speaking dorf in the southwest of what is now Ukraine, but during her lifetime was variously a part of Russia, and at other times Romania ... they left in the 1920's).

A few of many examples:
>> “her grandmother and grandfather (both Ukrainians) were taken by force by the Germans to Vienna , Austria. Their baby was born in Vienna”<<

Germany connection:
It the 1800’s many Germans were invited by the Czars to settle in “Russia”, (which at that time included Ukraine and many other areas). Shortly prior to, and during World War II, in an agreement between Stalin and Hitler, many were forcibly relocated back to Germany, Austria, and the Russian far east. During the 1950’s until recently Germany had a resettlement program that allowed many of those to return to Germany, with various aid.

Israel connection:
During Hitler’s regime many Jewish were transported to concentration camps, including some in Austria. There could be Jewish repatriation with Israeli immigration implications.

The more common situation:
If they are natively Ukrainian, then it’s a bit simpler: sorting out the laws of Austria and Ukraine.

You should ask the Austrian embassy in London (by your nickname, I assume that you reside in the UK).

The US counts as an American citizen anyone born on US soil. Most countries do NOT do this - what matters is the natinality of the parents. You would have to check with the nearest Austrian consulate or embassy but I very much doubt if your wife can claim Austraian citizenship.

The question is - why bother? Unless you divorce her status isn't going to be affected by gaining Austrian citizenship and within a few years she'll be able to obtain British citizenship.

The FPÖ has the majority of the votes already!
Not a chance for you anyway.