The objective of this study is to investigate the dynamic behaviour of a linear viscoelastic elliptical beam subjected to the vertical distributed loading by using the mixed finite method based on Timoshenko beam theory. It is assumed that, the linear viscoelastic material exhibits the standard type of distortional behaviour while having elastic Poisson's ratio. The finite element analysis is carried out in Laplace space, the material properties are implemented into the formulation through the use of the correspondence principle. The results are transformed back to the time domain numerically by using of the Modified Durbin's transformation algorithm. Through the analysis, two different types of impulsive load are considered, namely, isosceles triangular and right triangular impulsive load with the same duration and the maximum intensity of distributed load. A circular and two different elliptically oriented cross-sections are selected keeping the net cross-sectional areas equal to each other. The influence of different types of impulsive loads and cross-sections on the dynamic behaviour of viscoelastic elliptical planar beam with fixed-fixed boundary condition is investigated in detail and the examples are presented as original examples for the literature.