Preheat the oven to 350 degrees F (175 degrees C). Grease and flour two 9x5-inch loaf pans.
Sift flour, baking soda, and salt into a large bowl.
Cream sugar and butter together in a separate bowl. Stir in bananas, eggs, and walnuts until well blended.
Pour wet ingredients into flour mixture and stir just until blended. Divide the batter evenly between the two prepared pans.
Bake in the preheated oven until a paring knife inserted into the crown of each loaf comes out clean, 60 to 70 minutes.
Remove from the oven and let loaves cool in the pans for at least 5 minutes. Turn out onto a cooling rack, and let cool completely, about 30 minutes.
Slice and serve. For more intense flavor, wrap each loaf in aluminum foil to keep in the moisture, then refrigerate for at least 2 hours before serving.