A simple mathematical model of a nuclear reactor, which consists of only six nonlinear differential equations, was formulated. Using this model, a digital program for predicting the dynamic response of the loss-of-fluidtest (LOFT) reactor was developed. In addition, the application of a model-based Kalman filtering technique was considered. Results of the model calculation by the developed program were compared with the estimation results as well as those from actual test data taken during the anticipated transient without scram (ATWS) of LOFT. The comparison demonstrates the simple model``s phenomenological accuracy and the applicability of the estimation algorithm to nonlinear dynamic system. As well, the dependence on some parameters of the state estimation technique was investigated.