The half-normal distribution is one of the widely used probability distribution for non-negative data modeling, specifically, to describe the lifetime process under fatigue. In this paper, we introduce a new type of non-negative distribution that extends the half-normal distribution. We refer to this new distribution as the epsilon half-normal distribution. We provide mathematical properties of this new distribution. In particular, we derive the stochastic representation, explicit formulas for the n-th moment, the asymmetry and kurtosis coefficients and the moment generating function. We also discuss some inferential aspects related to the maximum likelihood estimation. We illustrate the flexibility of this type of distribution with an application to a real dataset of stress-rupture. © 2012 Elsevier B.V. All rights reserved.