The objective of the current work is to model and simulate some important components of the speech production system like vocal folds and vocal tract for the better and efficient speech generation. First of all, we develop an appropriate mathematical vocal folds model that simulates the process of the vocal folds by using fulcrum point. We incorporate rotary motion of the glottis by considering the moments of the glottis about the fulcrum point which is very similar to the seesaw motion about the fulcrum point. By changing the position of the fulcrum point, we have different scenarios for the motion of the glottis. The fulcrum point position has a significant role in determining the shape of the glottal flow. This fulcrum point approach has been examined with the cases of viscous and non-viscous flows and, forced and self-oscillatory motion of the vocal folds. In case of non-viscous flow, the vibration of the vocal folds is caused by the Bernoulli equation of the flow while in the cases of viscous flow, the motion of the vocal folds together with the solution of Navier-Stokes equations, simulate the flow within an idealized human glottis. Secondly, we develop a highly efficient 2D-featured 1D waveguide model for the vocal tract that is comparable with the standard 2D waveguide model. In this model, vocal tract has been decomposed into a number of convergent and divergent ducts. The divergent duct is modelled based on splitting the volume velocity into its axial and radial components while the convergent duct is represented by a one dimensional waveguide. The present model has been found to be more efficient than the standard 2D waveguide model and in very good comparison with it in the formant frequency patterns of the vowels /ɑ/, /e/, /i/, /ɔ/ and /ʊ/. The model has two control parameters, the wall and the glottal reflection coefficients, that can be effectively employed for the bandwidth tuning. New approaches for vocal folds and vocal tract present novel contribution in the fields of speech production.