In this study, a SVEIR-type compartmental model of Poliomyelitis transmission is examined under random effects. We introduce Generalized Beta and normal distributed random parameters into the equation system to investigate the random dynamics of the disease. The approximate analytical solution of the model under random effects is obtained by using Random Differential Transformation Method (RDTM). Results from simulations and RDTM are analyzed to comment on the randomness of the compartments and disease transmission. It is seen that the random model successfully provides similar results that can be obtained through the deterministic model while providing additional information on the random behavior of the disease, such as the standard deviations and the variation coefficients.