A robust algorithm to estimate three-dimensional strain in the left-ventricular heart wall, based on magnetic resonance (MR) grid-tagging in two sets of orthogonal image planes, is presented. Starting-point of this study was to minimize global interpolation and smoothing. Only the longitudinal displacement was interpolated between long-axis images. Homogeneous strain analysis was performed using small tetrahedrons. The method was tested using a stack of short-axis images and three long-axis images in six healthy volunteers. In addition, the method was subjected to an analytical test case, in which the effect of noise in tag point position on the observed strains was explored for normally distributed noise (0.5 mm RMS). In volunteers, the error in the longitudinal displacement due to interpolation between the long-axis image planes was -0.10 +/- 0. 48 mm (mean +/- SD). The resulting error in the longitudinal strain epsilon(l) was -0.003 +/- 0.02. The analytical test case was used to quantify the effects of three sources of errors on the observed strain. The SD of the difference between homogeneous strain and true strain was 0.06 for epsilon(r.) The error due to the 3-D reconstruction was 0.004 for epsilon(r.) The error in epsilon(r) resulting from simulated noise in the tag point position was 0.10. Equivalent results were obtained for all other strain parameters; thus, the error resulting from noise in the tag point position dominates the error introduced by approximations in the method. Because the proposed method uses a minimum of global interpolation and smoothing, it offers the prospect to detect small regions of aberrant contraction.