What is the expression to describe rising stock prices?

There are a couple of different terms that you could use to
describe this.

The term for a time when stock prices are rising is
"bull market." This is as opposed to a "bear market" in which stock prices
fall.

However, I see that you have tagged this with "Great
Depression" and so I assume that you are talking about that era. In the late 1920s, stock prices
were rising much faster than they ought to have. This can still be called a bull market, but we
also tend to use the term "bubble" in case like this. We say that there is a bubble in the stock
market when prices are rising more quickly than they ought to. The implication behind this term
is that the bubble will eventually pop (as it did in October 1929) and prices will then fall
severely.

So you can call rising prices a bull market (which does
not necessarily imply prices are rising too fast) or you can call the a bubble (which does imply
they are rising too fast).