Computed laminography (CL) was developed to use X-rays from synchrotron sources for high-resolution imaging of the internal structure of a flat specimen from a series of 2-D projection images. The projections are acquired by irradiation of the sample under different rotation angles where the object rotation axis is inclined with respect to the beam direction. This yields for laterally extended objects a more uniform average transmitted intensity during sample rotation compared with computed tomography (CT). The reconstruction problem of CL cannot be reduced to a data-efficient 2-D case (as for parallel-beam CT) since each single slice perpendicular to the rotation axis requires a 2-D region on the detector as input data for all projection directions. This paper describes a computationally efficient reconstruction procedure based on filtered backprojection (FBP) adapted to the CL acquisition geometry. From the Fourier slice theorem, we derive a framework for analytic image reconstruction and outline implementation details of the generic FBP algorithm. Different approaches reducing the reconstruction time by means of parallel and distributed computations are considered and evaluated.