This paper presents mechanical strength analysis of the critical components of the dosing pump. Due to the uneven stress distribution and high contact pressure created between the contacting surfaces the v-packing seals and the PTFE cup were subjected to failure. During the analysis of stresses, the critical components that are considered as a tri-layer compound cylinder such as the assembly of suction tube, PTFE cup, and the check seat and the assembly of plunger, v-packing seals and the spacer tube were analyzed based on the lame’s equation of compound cylinders. The materials that are used for making these components was 316 stainless steel and polytetrafluoroethylene or Teflon that are ductile in nature. The failure criteria’s which are adopted in this analysis were the maximum shear /Tresca criteria and the von-Mises criterias. To optimize the stress distribution in the compound cylinders a classical Lagrangian multiplier method was adopted based on the maximum shear stress theory. The analytically calculated results was compared with the finite element Ansys simulation software and results from the optimization technique shows that the uneven stress distributions were optimized.