We report a study of an elastic buckled beam undergoing a contactless magnetic actuation of Laplace type. The beam model is based on the elastica beam theory including the beam extensibility. The Laplace force is produced by an electric current travelling along the beam placed in a magnetic induction. The magnitude of the electric current is the control parameter and by increasing the electric current the beam switches from one stable state to the other one for a given beam end-shortening. The main purpose of the study is to investigate the bistable response, more precisely, the diagram of the electric current as function of the midpoint vertical displacement of the beam according to the magnet location along the elastic beam. The model equations are established and they are numerically solved using an algorithm developed for nonlinear boundary value problem. A second part of the study is devoted to experimental validation of the model and comparisons with the results extracted from the numerical solutions to the model equations. Especially, the comparisons ascertain with good accuracy the approach of the proposed bistable beam model. In addition, the influence of the model parameters on the bistable response is clearly identified.