In the improvement of pumpkins, the selection based on one or a few characters of interest tends to be less efficient, leading to a superior product only compared to the few characters selected. To maximize the simultaneous selection of multiple characteristics of interest, selection indexes are used to obtain a numerical value resulting from the combination of the characters on which the simultaneous selection is to be practiced. The objective of this study was to determine genetic parameters and the most appropriate selection indexes in strains of Summer squash (C. pepo). Statistical analyzes were performed based on 65 genotypes belonging to the vegetable germplasm bank of the Federal University of Uberlândia. The variables analyzed were: leaf area index, precocity, SPAD index, productivity. plant-1, number of fruits. Plant-1, leaf temperature, NDVI index and NDRE index. The indexes were used: Smith (1936) and Hazel (1943), the sum of “Ranks” by Mulamba and Mock (1978), and Willians (1962). The selection methodologies selected ten individuals (15% of the genotypes). The values found for h² (%) ranged from 36.92% (SPAD) to 59.65% (cycle). The values obtained in the CVg / CVe quotient were below 1, varying from 0.18 for leaf temperature to 0.70 for the cycle, with the other variables close to 0.5. The CVg genetic variation coefficient (%) was also low, ranging from 1.84% for leaf temperature to 30.94% for productivity. The greatest gains obtained with direct and indirect selection were for the characters productivity (35.92%), NDRE (33.04%), number of fruits (28.93%) and leaf area index (22.72%). The Mulamba and Mock (1978) index showed the highest total selection gain value, providing a balanced distribution of selection gains, choosing the genotypes: 8, 31, 34, 38, 42, 64, 65, 66, 67 and 68.