The assessment of the biomechanical properties of the skin using various imaging techniques has been used as a diagnostic tool in dermatology. Optical coherence elastography (OCE) is one of the techniques that allows for the measurement of elastic properties. OCE relies on measuring tissue displacements induced by external sources. Measuring the tissue's mechanical properties in vivo using OCE is often challenging due to bulk tissue movement. This study aimed to develop an OCE system that allows for minimizing the effects of bulk tissue movements. To achieve this, we designed a two-beam OCE system that simultaneously measures the tissue displacement at two locations on the sample. This allows for cancelling the effect of the tissue bulk movement, which is common to both measurement points. We used a piezoelectric transducer to generate surface acoustic waves (SAW) in the sample. The velocity of the excited waves, which is proportional to the rigidity of the sample, was measured by calculating the phase delay of the SAW at two locations on the sample. Simultaneous measurement at two locations was achieved by dividing a single light beam into two by focusing on the sample at two different locations. The two beams travel different optical path lengths, and the reflected signals were depth encoded in a single optical coherence tomography scan using a single reference beam. The system was characterized using different tissue-mimicking phantoms and the skin of healthy volunteers at the wrist and the palm. We achieved an approximately 50-fold increase in phase sensitivity measurement. We designed a simple two-beam OCE system that effectively minimizes the effect of tissue movement. We believe that the presented system will find immediate applications in the clinic to monitor the progression of systemic sclerosis disease.