For the hypergeometric function \[ F(a,b,c; z)= \sum^\infty_{n=0} {(a)_n(b)_n\over (c)_n(1)_n} z^n, \] the authors imposed restrictions on parameters \(a\), \(b\), \(c\) such that \(zF(a,b,c;z)\) will be various subclasses of uniformly starlike and uniformly convex functions.