A polynomial model of functions of lumped Markov's chains over finite field is represented. The authors represent a particular case of Markov's chains functions — the hidden Markov's models (HMM). A definition of the HMM stochastic equivalency was implemented based on stochastic matrix lumpability and asymptotic characteristics of HMM. The paper provides a polynomial representation of an equivalent HMM over the finite field GF(2<sup>n</sup>). It estimates a minimal order of the field GF(2<sup>n</sup>) for polynomial HMM representation, depending on the stochastic matrices implying vector size and possessing lumpability characteristic.