This note addresses the observer design problem for a class of second order distributed parameter systems. Particularly, second order distributed parameter systems without distributed damping (or non-strictly positive distributed damping) are studied. Based on finite number of measurements, exponentially stable observer is designed. The existence, uniqueness and stability of solutions of the observer are based on semigroup theory. The developed procedure is illustrated via an example. Numerical simulation results are included. Simulation results are in agreement with the theoretical results.