Real-time estimation of the modulus of elasticity (E) in paper machines would enable it to be controlled, improving final product quality and reducing the occurrence of sheet breaks. This paper develops a novel topology to estimate E on web machines based on an adaptive observer structure that combines model reference adaptive control with a closed-loop observer using field signals such as tension force, velocity/position, and torque. The evaluation of the proposed topology is performed on the dryer-calender span of the dry-end section of a lightweight coated paper machine. Results show a fast and accurate estimation of E, confirming the robustness of the adaptive observer structure.