In this article, we study the initial boundary value problem of generalized Pochhammer-Chree equation u t t - u x x - u x x t - u x x t t = f ( u ) x x , x ∈ Ω , t > 0 , u ( x , 0 ) = u 0 ( x ) , u t ( x , 0 ) = u 1 ( x ) , x ∈ Ω , u ( 0 , t ) = u ( 1 , t ) = 0 , t ≥ 0 , where Ω =(0,1). First, we obtain the existence of local W k,p solutions. Then, we prove that, if f ( s ) ∈ C k + 1 ( R ) is nondecreasing, f(0) = 0 and | f ( u ) | ≤ C 1 | u | ∫ 0 u f ( s ) d s + C 2 , u 0 ( x ) , u 1 ( x ) ∈ W k , p ( Ω ) ∩ W 0 1 , p ( Ω ) , k ≥ 1 , 1 < p ≤ ∞ , then for any T > 0 the problem admits a unique solution u ( x , t ) ∈ W 2 , ∞ ( 0 , T ; W k , p ( Ω ) ∩ W 0 1 , p ( Ω ) ) . Finally, the finite time blow-up of solutions and global W k,p solution of generalized IMBq equations are discussed.