We consider an inverse problem of determination of the coefficient k(x), x is an element of Omega in the second-order hyperbolic equation u(tt) = del(k(x)del u) in Omega(T) = Omega x (0, T) from the initial and boundary information u(x, 0), ut (x, 0) and k(x)del un vertical bar partial derivative Omega x ( 0,T). Here Omega subset of R-n is a rectangularly-shaped bounded domain and n is the outward unit normal to the boundary of Omega at the point x is an element of partial derivative Omega. We prove an existence and uniqueness theorem for the associated inverse coefficient hyperbolic problem. Our approach consists of monotonicity method based on integral relationships between the input and output data. Finally, we present various numerical results that show feasibility of our approach.