This paper describes a new method for shape and member-size optimization of a plane truss by using techniques of parametric curves. Description of nodal coordinates as well as cross-sectional areas in terms of Bezier curves enables one to find a smooth optimal truss. The optimal truss is found under the constraints such that all the response strains to multiple design loads including static loads and earthquake excitation are within a prescribed range. The objective function to be minimized is a weighted sum of the total structural mass and the deviation of the shape from the one preferred by the designer. The latter is written explicitly in terms of the coordinates of the control points. Side constraints are easily incorporated based on the convex hull property of the Bezier curve. In the examples, optimal trusses are found under single and multiple loading conditions and the characteristics of the optimal trusses in reference to the weight coefficients are discussed.