In this study, a multidimensional strain estimation method using biplane ultrasound is presented to assess local relative deformation (i.e., local strain) in three orthogonal directions in skeletal muscles during induced and voluntary contractions. The method was tested in the musculus biceps brachii of five healthy subjects for three different types of muscle contraction: 1) excitation of the muscle with a single electrical pulse via the musculocutaneous nerve, resulting in a so-called "twitch" contraction; 2) a train of five pulses at 10 Hz and 20 Hz, respectively, to obtain a submaximum tetanic contraction; and 3) voluntary contractions at 30, 60, and 100\% of maximum contraction force. Results show that biplane ultrasound strain imaging is feasible. The method yielded adequate performance using the radio frequency data in tracking the tissue motion and enabled the measurement of local deformation in both the vertical direction (orthogonal to the arm) and in the horizontal directions (parallel and perpendicular to direction of the arm) in two orthogonal cross sections of the muscle. The twitch experiments appeared to be reproducible in all three directions, and high strains in vertical (25 to 30\%) and horizontal (-20\% to -10\%) directions were measured. Visual inspection of both the ultrasound data, as well as the strain data, revealed a relaxation that was significantly slower than the force decay. The pulse train experiments nicely illustrated the performance of our technique: 1) similar patterns of force and strain waveforms were found; and 2) each stimulation frequency yielded a different strain pattern, e.g., peak vertical strain was 40\% during 10-Hz stimulation and 60\% during 20-Hz stimulation. The voluntary contraction patterns were found to be both practically feasible and reproducible, which will enable muscles and more natural contraction patterns to be examined without the need of electrical stimulation.