At the age of thirteen, she started studying Spanish Dance in the Higher Conservatory of Murcia, finishing her studies with Honours in 1995.
In 1996, she joined the Color Danza Company, which won the Ricard Moragues prize. In 1999, she joined the Andalusia Dance Company, directed by Jose Antonio, performing in a large number of shows choreographed by Javier Latorre, Eva Yerbabuena, Isabel Bayon, Alejandro Granadas and Javier Baron, among others.
In 2002, the company presented Bodas de Sangre for the Lorca and Granada Program, directed by Antonio Gades. In November of this year, she played one of the two leading parts in La Leyenda, by Jose Antonio.
In August 2004, El Sombrero de Tres Picos and El Café de Chinitas had their premiere directed by Jose Antonio in commemoration of the 100th anniversary of the birth of Dali.
In August 2004, El Sombrero de Tres Picos and Café de Chinitas, directed by Jose Antonio, were premiered, in commemoration of the hundredth anniversary of the birth~of Dali, for the Festivals of Castell de Peralada, Santander and San Sebastian. Elena Algado played the roles of the Water Carrier and the Flamenco Dancer respectively, in a cast that included Jose Antonio, Chano Domínguez and Esperanza Fernández.
In September 2004 she played in Asimetrtes, by Andres Martin, as part of the XIII Flamenco Biennial in Seville, a show that took part in the Festival La Maison de la Danse, in Lyon.
In November 2004, she joined the Ballet Nacional de España as Principal Dancer.
He has imparted several flamenco dancing workshops to members of the TEBNE at the Ballet Nacional de España, as well as master classes in different Conservatories and countries (Korea, Singapur,…).
In April 2012, Elena Algado and Miguel Ángel Corbacho, both have premiered their choreography “Tiempo de Sueños” at the XI Dance Open International Dance Festival Ballet Stars Gala, repeating next year 2013 with the premier of “Al Alma”, this time with the whole company.
Since September 2012, she carries out together with Miguel Ángel Corbacho the artistic direction of ENTREDOS BALLET ESPAÑOL and its first production choreography "Silencios Rotos".
In January 2013 she funds the “Centro Extremeño de Danza”, where she is the Director and imparts several dancing workshops.
In april 2014 Elena Algado together with Miguel Ángel Corbacho is invited to participate in the Gala of International Ballet Stars of the XIII Dance Open, and along with Miguel A Corbacho is asked to create and premier 3 new choreographys together with the worldwide known mezzosoprano Elina Garanca and the famous russian liryc bass Ildar Abdrazamov at the Opera and Ballet Gala of the 311th foundation Anniversary of the city of Saint – Petersburg (Russia).
In 2015 premiere at the Teatro Romano Baelo-Claudia "LAS MOIRAS" (The Fates) and also colaborate with pianist Manolo Carrasco in presenting his show "pianissimo" creating and performing some choreographies.
Currently , together with Miguel Angel Corbacho continues presenting to the audience “LAS MOIRAS” and "SILENCIOS ROTOS" and preparing new projects for 2016.