This paper proposes a closed analytical integration of BEM’s integrals in the contex of plane elasticity. Our BEM’s formulation is based on subparametric interpolation and problem’s geometry is discretized by straight elements with three nodes in the global coordinates system. Each element is transformed to a local dimensionless system, which uses a quadratic formulation. On this dimensionless system closed expressions for BEM’s integrals were developed by evaluating them with a Computer Algebra Systems (CAS). Quasi singular and singular integrals were addressed in our formulation and the analytical expression for them are able to deal with very strong quasi-singular situations (source point is very close to the integration element) and with cases when source point belongs to the element (singular integration). All those closed analytic expressions were optimized and implemented in a BEM code in substitution of numerical integration. This allows us to avoid expensive and repetitive calculations. A comparative study shows savings of 4000 % in CPU times for a BEM code based on analytical integration. Moreover, approximated solutions obtained by the BEM with analytic integration were more accurate than those produced by standard BEM codes.