I planted 4 cucumber plants in early June. They are growing vertically. There has been many many yellow flowers for quite some time now but not one of the plants have yet to produce a cucumber. WHY ?
The most likely reason is that they are not being pollinated.
Plants in the Cucurbitaceae family like cucumbers, squash and watermelon for example have separate male and female flowers. In order for cucumbers to form, the female blossoms must be pollinated with pollen from the male blossoms. The pollinator carriers are insects such as bees and each female flower may require from 15 – 20 visits to ensure an adequate pollination. If the flowers are not being pollinated it may because of a lack of pollinators. Weather can also affect pollination. Insects are less active during cloudy and wet weather. If there are few pollinating insects in your garden, you may have to hand pollinate. There are several how to demos on line to show you how to do this. If you go this route note the description below to differentiate male from female flowers. You should also be aware that the flowers open in the morning and pollen is viable for only that day, so if you are hand pollinating use pollen from a fresh male flower.
If there are sufficient pollinators, the issue may be with the flowers. The first flowers to form on the vine are male. The female flowers form later. Take a look at the flowers on your vines. The female flowers are usually single flowers and have a tiny cucumber structure at the base. The male flowers often grow in a cluster and have shorter stems. There has to be a mix of male and female flowers in order for pollination to occur. Wait to see if the newer flowers are female.
To increase production, hybrid varieties were developed to produce vines with mostly female flowers but seed companies include seeds in their packaging that will grow into vines with male flowers for pollination. These seeds may be dyed a different colour so you can identify them when planting. It is possible that none of your male flower vines grew so there is no pollen available.
For further information about growing cucumbers see:
https://extension.uga.edu/publications/detail.cfm?number=C934
http://www.omafra.gov.on.ca/english/crops/facts/cucumber_production.htm