An outline is given how to formulate a relativistic unitarized constituent quark model of mesons in momentum space, employing harmonic quark confinement. As a first step, the momentum‐space harmonic‐oscillator potential is solved in a relativistically covariant, three‐dimensional quasipotential framework for scalar particles, using the spline technique. Then, an illustrative toy model with the same dynamical equations but now oneqq¯and one meson‐meson channel, coupled to one another through quark exchange describing the3P0mechanism, is solved in closed form on a spline basis. Conclusions are presented on how to generalize the latter to a realistic multichannel quark/meson model. © 2003 American Institute of Physics