Modeling and analyzing pushbroom sensors commonly used in satellite imagery is difficult and computationally intensive due to the motion of an orbiting satellite with respect to the rotating Earth, and the nonlinearity of the mathematical model involving orbital dynamics. In this paper, a simplified model of a pushbroom sensor (the linear pushbroom model) is introduced. It has the advantage of computational simplicity while at the same time giving very accurate results compared with the full orbiting pushbroom model. Besides remote sensing, the linear pushbroom model is also useful in many other imaging applications. Simple noniterative methods are given for solving the major standard photogrammetric problems for the linear pushbroom model: computation of the model parameters from ground-control points; determination of relative model parameters from image correspondences between two images; and scene reconstruction given image correspondences and ground-control points. The linear pushbroom model leads to theoretical insights that are approximately valid for the full model as well. The epipolar geometry of linear pushbroom cameras is investigated and shown to be totally different from that of a perspective camera. Nevertheless, a matrix analogous to the fundamental matrix of perspective cameras is shown to exist for linear pushbroom sensors. From this it is shown that a scene is determined up to an affine transformation from two views with linear pushbroom cameras.