Japanese company Obayashi has declared that they will have a space elevator assembled by 2050. The elevator will spread 96,000 km (60,000 mi) into space 

and will transport people and shipment to a new space station. It will also work as a port to transport astronauts to Mars and beyond.

“The construction process consists of deploying the cable and constructing the

 facilities. It is necessary to analyze the cable dynamics in order to estimate the 

characteristics of the cable, counter-weight, facilities and climbers, and in order to determine the construction procedures.

Parameters for the cable dynamics include tension, displacement and elongation of the cable due to ascending climbers, masses of counter-weight and cable, wind, and fixed loads of facilities.

With the help of a computer simulation of the equations of motion, we 

designed the system and determined the construction process.” ~ Obayashi

Watch the video below to learn more about their model.