From a theoretical viewpoint, the vocal folds vibration affects the vocal tract transfer characteristics through nonlinear time-varying interaction between the glottis and vocal tract. However, ordinary speech processing systems have neglected those effects under the assumption of linearity of production systems. But if one tries to improve the voice quality to be more natural or human-like, it becomes crucial to investigate and model such effects. For this purpose, analytic exeriments were conducted on the vocal folds vibration effects [Ohmura et al., ICSLP96]. Based on these experimental results, two types of speech synthesis models are proposed: one is a wave function model in which formant energy dumping is given by a time window function. The other is a second-order nonlinear differential equation in which the formant energy dumping pattern is controlled by its friction term. Its performance was confirmed by a preference test on speech wave reconstruction. A speech sample set used in this test contains 60 sentences uttered by four speakers. Evaluators listened to two kinds of reconstructed speech samples: one is synthesized by the proposed method and the other is synthesized by an ordinary LPC-based method. Results show that the proposed method is clearly superior in its quality.