The preshaped curved beam is used as bistable mechanism in MEMS, its behavior is characterized by the snapping forces and stresses that evolve during deflection between the two sides of buckling. Based on analytical models, the influence of variating the material and dimension parameters on the behavior of the curved beam is analyzed. The limit of miniaturization of the beam based on the stress limits is identified. Further, a design optimization methodology is provided which allows selecting the miniature dimensions of the curved beam after defining the range of possible dimensions. This method ensures a required bistablity behavior in terms of stroke and holding forces, while respecting the design requirement. Several design constraints are defined including material and technological limitations and some other specifications. The results in different cases of optimization problems showed to be the same using a proposed optimization methodology and a standard gradient based optimization algorithm.