To ensure the safety of wooden structures, estimation of wood strength is based on the characteristicstrength values. The Brazilian standard (NBR, in Portuguese Norma Brasileira Regulamentadora) 7190 proposesequations to estimate the strength properties with a simplified procedure, which allows obtaining thecharacteristic values through relations that correlate different mechanical properties. Using these equations,the values of tensile (ft0,k) and shear (fv0,k) strength can be calculated in a simplified way from the compressivestrength (fc0,k) values. In the present work, 36 tropical hardwood species were evaluated for tensile, shear andcompressive strength in the direction parallel to the grain, with a total of 1296 experimental measurements,and the precision of the relations defined by the Brazilian standard was assessed using the analysis of variance(ANOVA) method. Two-parameter regression models, based on linear, exponential, logarithmic and geometricfunctions, were used as an alternative proposal for the estimation of the strength properties. The statisticalanalysis validated the proposed relations, with the linear (ft0,k) and geometric (fv0,k) regression models beingthe models of best fit, with the coefficients of determination (R2) equal to 63,02 % and 70,15 %, respectively.In addition, new simplified equations were suggested. The least squares method was used to determine theoptimal coefficient (α) for validation of the Brazilian standard equations. The obtained coefficients validatedthe tensile strength relationship (ft0,k = fc0,k / 0,77), but failed to validate the shear strength relationship (fv0,k =0,12∙ fc0,k). In the latter case, the obtained values were significantly higher (up to 91 % higher) when comparedto those estimated by the Standard