In this paper, modeling of human speech articulator dynamics and its motor control are presented. The model dynamics of human articulators consists of lip soft tissue around a mouth, combined with surrounding muscles and jaw bone structures. The lip soft tissue is modeled as a discrete model approximation composed of networked lumped nodal masses interconnected with adjacent ones via viscoelastic elements. Stiffness of each element is adjusted to ensure the compatibility in static deformation between the discrete model and its soft tissue prototype considering each compartment size. Muscle motor commands to drive the articulator model are estimated using a control strategy of mimicking human speech motion. An inverse dynamics algorithm based on Gradient Descent Search (GDS) selectively adjusts the muscle motor command in order to produce the reference speech motion. Simple articulatory motions of the model are demonstrated by the activation of muscle motor commands, estimated from the measured human articulatory motions.