Noise levels have rapidly increased in recent years, largely due to the proliferation of modern appliances and critical noise sources like engine exhaust mufflers. Controlling muffler-radiated noise could reduce its impact on the surrounding communities. Generally, conventional mufflers utilize expensive sound-absorbing, fibrous, porous materials with high cost and harmful effects. Thus, eco-friendly materials are being used as alternative materials for their lower cost and less effects. The objective of this study is to evaluate natural material fiber's potential as an effective sound absorber in exhaust absorptive mufflers. Also, evaluate an elliptical muffler's performance by studying several factors, including liner materials, liner thickness, and how these factors affect sound transmission loss. The finite element method is used to simulate and analyze the sound transmission loss of a three-dimensional elliptical muffler model built using COMSOL Multiphysics. This paper proposed an exhaust muffler model with a waste of (date palm trunk, coconut or coir, and corn fiber) as an eco-friendly sound-absorbing material. In addition, a parametric study with a frequency range of up to (6000) Hz was done to evaluate the effect of liner thickness and inlet/outlet tube diameter on transmission loss. The results indicated that airflow resistivity (Rf) is the effective factor that governs sound transmission loss; higher airflow resistivity materials provide better attenuation. Absorbing material with higher airflow resistivity showed an incremental rise in transmission loss beyond 500 Hz, with notable peaks appearing at (1.25, 2.5, 3.4 & 5) kHz.  Moreover, it is effective to reduce inlet/outlet diameter and increase liner thickness.