Relativistic multimode pseudo-Jahn-Teller effect (E-2' + (2)A(2)'') x (e' + a(2)'') is considered for planar tetratomic molecules YX3, which have the odd number of electrons and are characterized by the double symmetry group D-3h'. Our analysis is based on the symmetry properties of electronic Hamiltonian, which includes spin-orbit coupling terms. Taylor series expansion of electronic Hamiltonian in terms of vibration normal modes e' and a(2)'' is restricted by second order terms for electrostatic and spin-orbit contributions. The result of this research is 6 x 6 vibronic matrix, which depends on e' and a(2)'' vibration normal modes and includes nine electrostatic and ten spin-orbital real constant parameters.