The present invention is a cross-flow evaporator adapted to generate vapor from the heat of the exhaust gases from an internal combustion engine. The evaporator is constituted, among other elements, by two plates (1, 2) spaced from one another which contain chambers (1.1, 2.1). The heat exchange tubes (3) alternately communicate the chambers (1.1, 2.1) of both plates (1, 2) , establishing a specific path for the fluid intended to change phase. The tubes (3) extending between the chambers (1.1, 2.1) of the two plates (1, 2) are arranged transverse to the flow of the hot gas. This evaporator is suitable for heat recovery systems using a Rankine cycle, making use of the heat from the exhaust gases. The invention is characterized by a special configuration of the walls (2) which prevents the crack failure or damage caused as a result of the differential expansion between the exchange tubes (3) and said walls (2).