Abstract: The purpose of this paper is to study the existence of solutions to second order differential inclusions in Banach spaces, the problems discussed are as follows (1) if multifunction F satisfies some condition as (H1) ∃ M>0,∀ x1,x2,y∈v0,w0,x1≤x2,∀ u1∈F(t,x1,y),∀ u2∈F(t,x2,y), we have u2-u1≥-M(x2-x1) (H2) there exists const L,M>L≥0, for any x,∀ y1,y2∈v0,w0,y1≤y2,∀ v1∈F(t,x,y1),∀ v2∈F(t,x,y2), we have v1-v2≥-L(y2-y1) (H3) there exists const K,M> K> L,for any x,y∈v0,w0,x≤y,∀ u∈F(t,x,y),∀ v∈F(t,y,x), we have u-v≥(K+L)(y-x) (H4) for ∀ uF∈F(t,v0,w0),∀ vF∈F(t,w0,v0), we have -vő+L(w0-v0)≤uF, v0(0)≥v0(1)=θ -wő-L(w0-v0)≥vF, w0(0)≤wo(1)=θ we get the result that there is a solution in v0,w0 to inclusion (1). The resluts presented in this paper generalize results in and simplify the proof to.