Stack traces are not vulnerabilities by themselves, but they often reveal information that is interesting to an attacker. Attackers attempt to generate these stack traces by tampering with the input to the web application with malformed HTTP requests and other input data.
If the application responds with stack traces that are not managed it could reveal information useful to attackers. This information could then be used in further attacks. Providing debugging information as a result of operations that generate errors is considered a bad practice due to multiple reasons. For example, it may contain information on internal workings of the application such as relative paths of the point where the application is installed or how objects are referenced internally.
There are a variety of techniques that will cause exception messages to be sent in an HTTP response. Note that in most cases this will be an HTML page, but exceptions can be sent as part of SOAP or REST responses too.
Some tests to try include:
All the above tests could lead to application errors that may contain stack traces. It is recommended to use a fuzzer in addition to any manual testing.
Some tools, such as OWASP ZAP and Burp proxy will automatically detect these exceptions in the response stream as you are doing other penetration and testing work.
Search the code for the calls that cause an exception to be rendered to a String or output stream. For example, in Java this might be code in a JSP that looks like:
<% e.printStackTrace( new PrintWriter( out ) ) >
In some cases, the stack trace will be specifically formatted into HTML, so be careful of accesses to stack trace elements.
Search the configuration to verify error handling configuration and the use of default error pages. For example, in Java this configuration can be found in web.xml.
 ZAP Proxy - https://www.owasp.org/index.php/OWASP_Zed_Attack_Proxy_Project