The Zlotys 125m ($US 36.9m) order is being co-financed by the European Union (EU) through the Operational Programme Infrastructure and Environment.
The 100km/h vehicles will be fitted with cranes and snow-clearing equipment.
PKP PLK says it is investing in new vehicles to improve safety at worksites and speed up infrastructure maintenance.
The first six vehicles will be delivered before the end of the year to PKP PLK depots in Bydgoszcz, Lodz, Walbrzych, Krakow, Gydnia, and Poznan.
In addition to the 36 vehicles from ZPS, PKP PLK is planning to order new road-rail vehicles, plain line and turnout tampers and ballast profilers by 2021.