Point-wise 3D displacement measurements over time are a key input for monitoring shotcrete shells during construction according to the New Austrian Tunneling Method. This book is a state-of-the-art contribution to tunnel monitoring. We use displacement measurements to construct their field histories, by two diverse interpolation strategies: one in a fixed Cartesian base frame and the other in a moving cylindrical base frame. Thin shell kinematics and a micro-viscoelasticity model for hydrating shotcrete allow for estimation of strain and stress field histories. Thereby, the moving base frame interpolation gives more realistic estimate of the actual load carrying behavior of a tunnel. We study the influence of shotcrete composition on the estimation of shell stresses: a realistic estimate of stresses require a more accurate shotcrete composition, while the estimate of utilization degree is too robust to be affected by the shotcrete composition. A solution of partial differential equations for equilibrium in cylindrical coordinates reveals that, for a tunnel in clayey ground at moderate depth, the maximum shear tractions at the ground-shell interface may even exceed the normal ones.