An ironing press of the type wherein the stationary ironing board is heated by a heating plate lowered onto it by an arm pivotally secured to the press body. To allow freedom of movement in all directions of the heating plate with reference to the ironing board, there is associated with a central multidirectional pivotal connection between the heating plate and the carrier arm, an elastic connection constituted by coaxially bored bosses raised on the plate, the bores in said bosses being engaged by pivots elastically fitted on the carrier arm at points lying with the pivotal connection on a line parallel with the pivotal axis between the heating plate and the carrier arm.