The present study provides a comprehensive model for flame profile parameters of horizontal turbulent jets, including the flame horizontal projection distance, the flame vertical height, the flame trajectory and the flame cross section radius, which have not been completely quantified previously. Experiments are carried out with circular nozzles (diameter: 3, 4, 5, 6 mm) employing propane as fuel with a wide range of discharge velocity, which covers both buoyancy- and momentum-controlled jet conditions. Similarity analysis of the fluid dynamics is developed to determine the flame horizontal projection distance and flame vertical height in terms of the initial jet momentum and an effective buoyancy of the flame, which together determine a characteristic length scale and a characteristic volumetric flow rate for interpreting the data. Moreover, an integral model based on top hat similarity of the flow profiles is derived to support the non-dimensional analysis, and in addition to predict the flame trajectory and flame cross section radius. The integral model includes equations for air entrainment and for momentum conservation of the flow, where both the normalized flame horizontal projection distance and the normalized flame vertical height show asymptotic behaviors consistent with small initial momentum condition and large initial momentum condition, respectively. The proportionality constants of the top hat similarity profiles are determined based on the developed theory and the experimental data, from which also an effective entrainment coefficient is derived and the flame cross section radius is resolved. The present study provides new similarity analysis and a comprehensive model for the flame profiles of horizontal turbulent jets. (C) 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.