Let G(t)\(\in L(X,X)\), \(t\geq 0\) be a strongly continuous semigroup of bounded linear operators in a separable Banach space X with the infinitesimal generator A, \(T>0\), and let F be a set-valued map from [0,T]\(\times X\) into closed nonempty subsets of X. A continuous function x: [0,T]\(\to X\) is called a mild trajectory of the differential inclusion \(x'\in Ax(t)+F(t,x(t))\) if there exist \(x_ 0\in X\) and a Bochner integrable function f: [0,T]\(\to X\) such that f(t)\(\in F(t,x(t))\) a.e. in [0,T] and the function x(t) satisfies the integral equation \(x(t)=G(t)x_ 0+\int^{t}_{0}G(t-s)f(s)ds.\) The author studies mild trajectories of the above differential inclusion problem and shows that under some technical assumptions the mild trajectories of the given problem form a dense set in the mild trajectories of the convexified differential inclusion problem \(x'\in Ax+\overline{co} F(t,x),\) \(x(0)=x_ 0\).