Variational auto-encoders (VAE) are popular deep latent variable generative models which are trained by maximizing an Evidence Lower Bound (ELBO). To obtain tighter ELBO and hence better variational approximations, it has been proposed to use importance sampling to get a lower variance estimate of the evidence. While it has been suggested many times in the literature to use more sophisticated algorithms such as Annealed Importance Sampling (AIS) and its Sequential Importance Sampling (SIS) extensions, the potential benefits brought by these advanced techniques have never been realized for VAE.Taking inspiration from the MCMC and the normalizing flows literature, we present here the Monte Carlo Variational Auto Encoder which is based on a novel representation of Markov kernels.