This work investigates the use of an Echo State Network (ESN) to predict turbulent jet flow behavior. ESNs are a particular class of Recurrent Neural Networks (RNNs) that have been shown to model transient chaotic systems while avoiding some of the difficulties associated with training other types of recurrent neural networks. It is a large, random, fixed recurrent neural network in which each neuron receives a non-linear input signal, and the weights of the input and hidden neurons are fixed randomly. An extensive literature review is performed regarding the history of turbulent jet modeling and the use of an ESN to model turbulent flow analogs. In an initial investigation, a turbulent free jet issuing from a circular tube into a quiescent medium was modeled using an ESN. ESN training was achieved using a validated LES dataset obtained from commercially available CFD software. A separate LES dataset was used to evaluate how well the ESN predicted flow field behavior. A hyperparameter search was undertaken to enhance the ESN's ability to model the turbulent flow field under consideration. The ESN model proved capable of reproducing instantaneous vortical structures and centerline velocity behavior relative to LES model data and previously published experimental data. In a second investigation, two cases of heated turbulent jets discharging from a nozzle to a cold surrounding were studied using an ESN. LES of the jets were carried out in commercial CFD software, and the data obtained from LES were used for training and testing the ESN. Detailed comparisons of the mean velocity profiles and the mean temperature profiles along the streamwise and radial directions were provided, along with turbulence quantities. ESN showed a good agreement with LES simulation and the experiment data. The coherent structure of the jet was investigated by the visualization of the isosurface of the Q criterion. ESN was shown to be efficient in capturing the vortex rings at the vicinity of the nozzle. The ESN also proved capable of capturing mean turbulent kinetic energy distribution for different temperature gradient values. In the third and final investigation, the model problem was a variable density jet originating from a cylindrical tube that passed through a weakly restricted co-flow of low-speed air streams. ESN training and testing were carried out with the help of a validated LES dataset obtained from commercial CFD software. Compared to LES model data and previously published experimental data, the ESN model was able to reproduce turbulent flow field statistics. The ESN model correctly reproduced the profile shapes of radial shear stresses. The vortical evolution for the Helium jet was studied with the ESN model, and the ESN model captured the vortex rings formed at the jet exit and the large-scale structures downstream of the jet. Based on the study, it was concluded that the ESN model has the potential to model turbulent flow fields effectively.