Two classical civil engineering inverse problems are considered. The first deals with the determination of dynamic moving loads applied to a reinforced concrete beam. The second one corresponds to the monitoring and the damage assessment. The concrete damage due to overloading is modeled by a loss of the concrete Young' modulus, whereas the steel bar damage due to corrosion effects is modeled by a reduction of the steel bar cross section. To identify the loading and damage parameters, deterministic and probabilistic model updating techniques are applied and compared. In the deterministic approach, a gradient descent technique based on the adjoint framework is used to minimize the data misfit functional with a Tikhonov regularization term. Then, a regularization by a means of Bayes's rule is considered in a probabilistic approach. The estimation is of the minimum variance type achieved with the help of the transformed ensemble Kalman filter.