Resonant Acoustic Rheometry (RAR), a newly developed ultrasound-based technique for non-contact characterization of soft viscoelastic materials, has shown promise for quantitative viscoelastic assessment of temporally changing soft biomaterials in real time, and may be used to monitor blood coagulation process. Here, we report the development of a novel, multichannel RAR (mRAR) system for simultaneous measurements of multiple temporally evolving samples and demonstration of its use for monitoring the coagulation of multiple small-volume plasma samples. The mRAR system was constructed using an array of 4 custom-designed ultrasound transducers at 5.0 MHz and a novel electronic driving system that controlled the generation of synchronized ultrasound pulses for real time assessment of multiple samples simultaneously. As a proof-of-concept of the operation of the mRAR system, we performed tests using pooled normal human plasma samples and anti-coagulated plasma samples from patients treated with warfarin with a range of International Normalized Ratio (INR) values as well-characterized samples with different coagulation kinetics. Our results show that simultaneous tracking of dynamic changes in 4 plasma samples triggered by either kaolin or tissue factor was achieved for the entire duration of coagulation. The mRAR system captured distinct changes in the samples and identified parameters including the clotting start time and parameters associated with the stiffness of the final clots that were consistent with INR levels. Data from this study demonstrate the feasibility of the mRAR system for efficient characterization of the kinetic coagulation processes of multiple plasma samples.