A drilling system provides indications of the lithology of the formation being drilled by dynamically measuring at least one parameter of interest that is affected by the lithology of the formation being drilled. Suitably positioned sensors make dynamic measurements of parameters such as downhole weight on bit, bit torque, bit revolutions, rate of penetration and bit axial acceleration. One or more processors use the sensor measurements in conjunction with predetermined lithological models to determine whether the measurements indicate a change in formation lithology. Suitable models can be on derived expressions such as rock drillability, drilling response, dynamic drilling response, normalized or dimensionless torque; and formation shear strength. The lithological indications provided by the processor can be used to adjust drilling parameters, steer the BHA, monitor BHA health, and provide depth locations for bed boundaries and formation interfaces.