Tagged magnetic resonance imaging (tMRI) is a well-established method for evaluating regional mechanical function of the heart. Many techniques have been developed to compute 2D or 3D cardiac deformation and strain from tMRI images. In this paper, we present a new method for measuring 3D plus time biventricular myocardial strain from tMRI data. The method is composed of two parts. First, we use a Gabor filter bank to extract tag points along tag lines. Second, each tag point is classified to one of a set of indexed reference tag lines using a point classification with graph cuts (PCGC) algorithm and a motion compensation technique. 3D biventricular deformation and strain is computed at each image time frame from the classified tag points using a previously published finite difference method. The strain computation is fully automatic after myocardial contours are defined near end-diastole and end-systole. An in-vivo dataset composed of 30 human imaging studies with a range of pathologies was used for validation. Strains computed with the PCGC method with no manual corrections were compared to strains computed from both manually placed tag points and a manually-corrected unwrapped phase method. A typical cardiac imaging study with 10 short-axis slices and 6 long-axis slices required 30 min for contouring followed by 44 min of automated processing. The results demonstrate that the proposed method can reconstruct accurate 3D plus time cardiac strain maps with minimal user intervention.