The perturbation method has been used to measure stiffness of the human arm with a manipulator. Results are averages of stiffness during short perturbation intervals (less than 0.4 s), and also vary with muscle activation. We, therefore, propose a novel method for estimating static arm stiffness from muscle activation without the use of perturbation. We developed a mathematical muscle model based on anatomical and physiological data in order to estimate joint torque solely from EMG. This model expresses muscle tension using a quadratic function of the muscle activation and parameters representing muscle properties. The parameters are acquired from the relation between EMG and measured torque. Using this model, we were able to reconstruct joint torque from EMG signals with or without co-contraction. Joint stiffness is directly obtained by differentiation of this model analytically. We confirmed that the proposed method can be used to estimate joint torque, joint stiffness, and stiffness ellipses simultaneously for various postures with the same parameters and produces results consistent with the conventional perturbation method.