Let P [ A , B ] , − 1 ≤ B < A ≤ 1 , be the class of functions p such that p ( z ) is subordinate to 1 + A z 1 + B z . Let P ( α 1 ) be the class of functions with positive real part greater than α 1 , 0 ≤ α 1 ≤ 1 . It is clear that p [ A , B ] ⊂ P ( 1 − A 1 − B ) ⊂ P [ 1 , − 1 ] . The principal results in this paper are the determination of the radius of β -starlikeness and β -convexity of f ( z ) with β = 1 − A 1 − B , when f ( z ) is restricted to certain classes of univalent and analytic functions related vith P [ A , B ] .