We present an analytical model that describes the evolution of two consecutive interplanetary coronal mass ejections (ICMEs), their interaction, and the evolution of the merged region. In this model, the coronal mass ejections (CMEs) are seen as velocity and density (mass loss rate) fluctuations of the solar wind that result in the formation of shocks traveling into the ambient solar wind (ASW). The dynamical evolution of these structures depends on both the CME parameters such as the initial velocity, density, and the duration of the eruption as well as the solar wind conditions (ejection velocity and mass loss rate). The probability of an interaction of two consecutive CMEs launched in the same direction is high, basically depending on their speeds and the interval of time between the CMEs. As a result of the interaction, a merged region is formed. Its dynamical evolution is also addressed by the present model. Given a set of initial CMEs and ASW conditions, our model is able to predict the time and distance of the interaction between the ICMEs and the velocity of the merged region as a function of the heliospheric distance. These are fundamental parameters of space weather predictions. Also, the model is able to predict the arrival time and velocity of the merged region at 1 AU. In this work, we validate the model through its application to well documented interaction events observed on 2007 January 24, 2010 May 23, 2010 August 01, and 2012 November 09.