A new method for estimation of current-source density (CSD) from local field potentials is presented. This inverse CSD (iCSD) method is based on explicit inversion of the electrostatic forward solution and can be applied to data from multielectrode arrays with various geometries. Here, the method is applied to linear-array (laminar) electrode data. Three iCSD methods are considered: the CSD is assumed to have cylindrical symmetry and be (i) localized in infinitely thin discs, (ii) step-wise constant or (iii) continuous and smoothly varying (using cubic splines) in the vertical direction. For spatially confined CSD distributions the standard CSD method, involving a discrete double derivative, is seen in model calculations to give significant estimation errors when the lateral source dimension is comparable to the size of a cortical column (less than approximately 1 mm). Further, discontinuities in the extracellular conductivity are seen to potentially give sizable errors for even wider source distributions. The iCSD methods are seen to give excellent estimates when the correct lateral source dimension and spatial distribution of conductivity are incorporated. To illustrate the application to real data, iCSD estimates of stimulus-evoked responses measured with laminar electrodes in the rat somatosensory (barrel) cortex are compared to estimates from the standard CSD method.