Let S(p，α)，C(p，α) and K(p，α) denote the classes of p-valent starlike，convex and close-to-convex functions of order α respectively. In this paper the extreme points and support points of these classes are studied and a series of results have been obtained as follows: Theorem 1.(l) SuppS(p，α)=EHS'(p,α); (2) SuppC(p，α)=EHC(p，α); (3) SuppK(p，α)?EHK(p，α). Theorem 2.(1)EHs(S(p,α))={xz^p/(1?yz)^2(1?α)p,│x│=│y│=1}(0≤α≤1/2). （2）Supp{s(S(p,α))J}=EHs(S(p,α))(0≤α<1/2). Where J is a continuous linear functional on which does not have the form J(h)=ΣA_nh⁽ⁿ⁾(0) for each h belonging to.