Electro and magneto-rheological shock absorbers made most attractive choice of semi-active vibration control systems. A mg fluid damper is a system in the magnetic fluid where a damper is filled with a magnetic fluid. A magneto-rheological fluid damper is a system where a damper is filled with a magnetic fluid. Within this system the external current (voltage) regulating the magnetic field varies as an electromagnet in the magnetic fields of the piston within the damper. By adjusting the magnetic strength of the piston, the damping force of the damper is controlled. This paper offers a conceptual mathematical method for analyzing the behaviour, by combining fluid-mechanic approach to the fundamental equation of Herschel-Bulkley, of the field controllable electro-and magneto-rheological fluid flow through the parallel plate duct. Electro and magneto-rheological shock absorbers are built with simple expressions for the pressure drop solution. The quasi-stable flow study from Herschel-Bulkley would then be extended to include accumulator pressure, shear thickening and shear thinning effects. This, thus, accounts for the nonlinear dynamic electro and magneto-rheological fluid damper behaviour. Non-dimensional plug thickness is calculated for the creation of simpler descriptions for the exact model. This article offers a theoretical model of magneto-rheological dampers that regulate the area to predict the established behaviour. This has been shown to be an electro and magneto-rheological fluid threshold modeling device, with the simplified H-Bulkley model for parallel plates. The results of the assessments show that the most promising magneto-rheological damper with less than 3 percent of the relative maximum errors are modern semi-active instruments for structural seismic response observed.