In this paper, by using the mountain pass lemma and the skill of truncation function, we investigate the existence and concentration phenomenon of nontrivial weak solutions for a class of elastic beam differential equation with two parameters λ and μ when the nonlinear term satisfies some growth conditions only near the origin. In particular, we obtain a concrete lower bound of the parameter λ, and analyze the relationship between λ and μ. In the end, we investigate the concentration phenomenon of solutions when μ→0, and obtain a specific lower bound of the parameter λ which is independent of μ.