We characterize the behavior of modes propagating along a hollow elliptical waveguide with lossy metamaterial cladding. The proposed metamaterial-dielectric elliptical waveguide supports surface-plasmon polariton (SPP) and hybrid ordinary-SPP modes in the operating frequency ranges. Previous studies on metamaterial-dielectric elliptical waveguides either ignore the effect of energy loss on the modes characteristics or employ approximate approaches to characterize modes behavior. Although some previous works include energy loss, they do not specify SPPs propagation versus hybrid-ordinary SPPs propagation in the operating frequency ranges. Here, we consider energy loss in the waveguide to eliminate errors resulting from neglecting the loss. Our waveguide structure facilitates SPP and hybrid ordinary-SPP modes propagation along the waveguide, has better energy confinement, and higher propagation length than previous results in the literature. In the elliptical waveguide, the propagation coefficient changes by changing the waveguide eccentricity; therefore, the elliptical nature of the studied waveguide facilitates its applications in pressure optical sensors.