In this experimental study, a novel continuous detonation phenomenon was investigated, where the detonation waves shuttle transversely within a linear channel combustor, normal to the reactant injection direction. A parametric study on this shuttling transverse detonation was conducted by varying the mixture of oxygen, nitrogen, and ethylene, and hence the equivalence ratio and oxygen volumetric percentage. In addition, fast-response wall pressure measurements and high-speed imaging were employed concurrently to measure the properties of the shuttling transverse detonation waves. Through these measurements, the shuttling transverse detonation features, wave modes, and wave dynamics were elucidated. The minimum oxygen volumetric percentage required to successfully establish shuttling transverse detonation was determined to be 44.7%. Depending on the testing conditions, four different wave modes of the shuttling transverse detonation, three to six-wave modes, were observed. The velocities of the shuttling transverse detonation waves had deficits relative to the ideal Chapman-Jouguet detonation wave velocities. To scale the wave mode dynamics of the shuttling transverse detonation, the wave velocity of the shuttling transverse detonation normalized by two times of the longitudinal filling velocity of the reactant mixture, a dimensionless quantity, was used. The values of this dimensionless quantity are in a range of 1.8–2.6 for the current experiments. The experimental results indicate that, in addition to the reactant injection flow dynamics, more physical quantities related to the reactant mixture properties and quality need to be studied further as they can influence the wave dynamics of the shuttling transverse detonation.