The stack H_{g,w} of hyperelliptic Weierstrass points is a degree 2g + 2 \'etale cover of the stack H_g of smooth hyperelliptic curves. The integral Chow rings of H_g and H_{g,1} have be previously calculated. In this talk, we explain how to compute integral Chow ring of each of these stacks H_{g,n}^w parametrizing hyperelliptic curves with n marked Weierstrass points along with a geometric interpretation of its generators. This is joint work with Dan Edidin.