We develop a biologically-plausible feedforward neuromechanical model for running insects that includes a simplified hexapedal leg geometry with agonist-antagonist muscle pairs actuating each leg joint. It is driven by a neural network modeling the central pattern generator (CPG) and the motoneurons which activate the muscles. This final goal is achieved in three stages. First, a relatively simple mechanical hexapedal model is constructed in which the joint torques are produced via actuated linear torsional springs with constant stiffness. In the second stage, this system is upgraded to a muscle-actuated hexapedal model in which each joint is actuated by a pair of agonist-antagonist Hill-type muscles. Muscles are driven by stylized action potentials that are characteristic of fast motoneurons, and modeled using an activation function and nonlinear length and shortening velocity dependence. In the final stage, the full neuromechanical model is obtained by integrating the above muscle-actuated hexapedal model with a CPG-motoneuron complex, feedforward input to the muscles now being supplied by action potentials from motoneurons. Restricting to dynamics in the horizontal plane and neglecting leg masses, we reduce the model (at each stage) to three degrees of freedom describing translational and yawing motions of the body. Collectively for all the models, parameter values are based on measurements from depressor motoneurons and muscles, and observations of kinematics and dynamics of the cockroach Blaberus discoidalis. Specifically, actuation inputs for the mechanical and muscle-actuated models are chosen to approximately achieve joint torques that are consistent with measured ground reaction forces. This is done by optimizing the time-dependent torque-free joint angles in the first model, and by optimizing motoneuronal outputs and muscle force levels in the second and third models. We show that the model (at each stage) has stable double-tripod gaits over the animal's speed range and that its dynamics at preferred speeds matches those observed. Using the various models, we further demonstrate that the system maintains stable gaits, with low frequency yaw deviations, when subject to impulsive force perturbations and random perturbations in foot touchdown (TD) position, foot TD and lift-off timing, and action potential (AP) input timing. The results are explained in terms of the low-dimensional dynamics. We also show that the model can be steered using stride-to-stride control strategies such as modifying foot TD positions and changing the number of motoneuron APs. In future, the integrated feedforward neuromechanical model developed in this thesis should act as a platform for studying different feedback strategies, and testing other biological hypotheses.