A system for determining the shape and position of an underwater riser extending from a floating platform, comprising: - an electronic processing unit installed on the floating platform or on the riser, said processing unit being configured to calculate a deformed shape of the riser by means of a numerical model of the deformed shape of the riser as a function of a plurality of acceleration values and of a plurality of position values in predetermined points of the riser, - a plurality of detection modules fixed to the riser in detection points along a longitudinal extension of the riser and in signal communication with the electronic processing unit, wherein said detection modules comprise detection modules with at least one accelerometer which is configured to detect an acceleration value of the respective detection point and to communicate it to the processing unit, characterized in that: - said detection modules comprise detection modules with at least one pressure sensor which is configured to detect a pressure value of the water in the respective detection point and to communicate it to the processing unit, - said processing unit is configured to calculate said position values as a function of the measured pressure values of the water, - the system comprises one or more detectors for detecting a relative position vector value between the floating platform and a detection module positioned at an upper end portion of the riser, said one or more detectors being in signal connection with the processing unit and - the processing unit is configured to calculate the position values of the detection points and/or the position of the floating platform also as a function of the detected relative position vector value, - said one or more detectors are selected in the group consisting of: - optical, acoustic or electromagnetic waves relative positioning sensors, one or more lasers, radars, cameras, extensometers, inclinometers, - displacement sensors of a telescopic joint connected between the floating platform and the upper end portion of the riser, - one or more detectors of the stroke and/or inclination of a tension cylinder or double acting telescopic cylinder connected between the floating platform and the upper end portion of the riser. - an electronic processing unit installed on the floating platform or on the riser, said processing unit being configured to calculate a deformed shape of the riser by means of a numerical model of the deformed shape of the riser as a function of a plurality of acceleration values and of a plurality of position values in predetermined points of the riser, - a plurality of detection modules fixed to the riser in detection points along a longitudinal extension of the riser and in signal communication with the electronic processing unit, - said detection modules comprise detection modules with at least one pressure sensor which is configured to detect a pressure value of the water in the respective detection point and to communicate it to the processing unit, - said processing unit is configured to calculate said position values as a function of the measured pressure values of the water, - the system comprises one or more detectors for detecting a relative position vector value between the floating platform and a detection module positioned at an upper end portion of the riser, said one or more detectors being in signal connection with the processing unit and - the processing unit is configured to calculate the position values of the detection points and/or the position of the floating platform also as a function of the detected relative position vector value, - said one or more detectors are selected in the group consisting of: - optical, acoustic or electromagnetic waves relative positioning sensors, one or more lasers, radars, cameras, extensometers, inclinometers, - displacement sensors of a telescopic joint connected between the floating platform and the upper end portion of the riser, - one or more detectors of the stroke and/or inclination of a tension cylinder or double acting telescopic cylinder connected between the floating platform and the upper end portion of the riser. - optical, acoustic or electromagnetic waves relative positioning sensors, one or more lasers, radars, cameras, extensometers, inclinometers, - displacement sensors of a telescopic joint connected between the floating platform and the upper end portion of the riser, - one or more detectors of the stroke and/or inclination of a tension cylinder or double acting telescopic cylinder connected between the floating platform and the upper end portion of the riser.