The light polarization properties provide relevant information about linear–optical media quality and condition. The Stokes–Mueller formalism is commonly used to represent the polarization properties of the incident light over sample tests. Currently, different Stokes Polarimeters are mainly defined by resolution, acquisition rate, and light to carry out accurate and fast measurements. This work presents the implementation of an automatic Stokes dynamic polarimeter to characterize non-biological and biological material samples. The proposed system is configured to work in the He-Ne laser beam’s reflection or transmission mode to calculate the Mueller matrix. The instrumentation stage includes two asynchronous photoelastic modulators, two nano-stepper motors, and an acquisition data card at 2% of accuracy. The Mueller matrix is numerically calculated by software using the 36 measures method without requiring image processing. Experiments show the efficiency of the proposed optical array to calculate the Mueller matrix in reflection and transmission mode for different samples. The mean squared error is calculated for each element of the obtained matrix using referenced values of the air and a mirror. A comparison with similar works in the literature validates the proposed optical array.