Photonic active devices exploit the interaction of light with other physical effects such as carrier, fields, power density, stress, temperature, or sound. The Stimulated Brillouin scattering (SBS) in optical waveguide is an important nonlinear effect results from the coherent interactions between optical and acoustic modes. The SBS can be considered as a primary obstacle effect in limiting the power scaling in many high power photonic devices because it normally has a lower threshold than other nonlinear effects. However, it is also well known that the interaction of light and sound can be exploited in several key applications. The guiding of acoustic wave in of optical waveguides allow interactions of light wave with the related phenomena of Brillouin Scattering (BS), Stimulated Brillouin Scattering (SBS) and Guided Acoustic Wave Brillouin Scattering (GAWBS). This thesis describes and studies the characteristics of different acoustic modes in optical waveguides by using the finite element method (FEM). A numerical approach based on the versatile FEM has been developed and employed for the analysis of acoustic modes in optical waveguides and also their interactions with optical modes. The high and low index contrast waveguides which can be designed, fabricated and optimized for different applications. The detailed spatial variations of the transverse and longitudinal displacement vectors are shown for longitudinal, bending, torsional, radial and torsional-radial modes in these waveguides. The vectorial acoustic modes in optical waveguides are shown for both the high and mlow index contrast silica waveguide along with their dispersion curves, the displacement vectors for transverse and longitudinal movements and the modal hybridness have been mdetermined and shown. Stimulated Brillouin Scattering (SBS) frequencies are also reported here for subwavelength size silica, Ge-doped rectangular and silicon slot optical waveguides. Variation of the displacement vectors, modal hybridness, and modal dispersion are also shown. A finite element based computer code is developed using a full vectorial acoustic model and combining this with another full vectorial optical model, the interaction between acoustic and optical modes are presented here and their overlap integrals have also been calculated.